Answer:
[tex]x_{1=} \frac{-1+i\sqrt{35} }{6} \\\\x_{2=} \frac{-1-i\sqrt{35} }{6}[/tex]
Step-by-step explanation:
Using the quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]
We will have two solutions:
[tex]x_{1}\\ x_{2}[/tex]
-3x^2-x-3=0 a=-3 b=-1 c=-3
We have:
[tex]x_{1}=\frac{1+\sqrt{-35} }{-6}\\\\x_{2}=\frac{1-\sqrt{-35} }{-6}\\[/tex]
we can write:
[tex]x_{1}=\frac{-1+\sqrt{-35} }{6}\\\\x_{2}=\frac{-1-\sqrt{-35} }{6}\\[/tex]
The solutions are not real numbers.
So, we know: [tex]i=\sqrt{-1}[/tex]
Finally we have:
[tex]x_{1}=\frac{-1+i\sqrt{35} }{6}\\\\x_{2}=\frac{-1-i\sqrt{35} }{6}\\[/tex]
Select the correct answer from the drop-down menu.
Consider the equations y=√x and y=x² -1
The system of equations is equal at approximately
A.(1.5,1.2)
B.(-1.5,-1.2)
C.(1.5,-1.2)
D.(-1.5,1.2)
Answer:
Choice A.
Step.-by-step explanation:
y=√x
y=x² -1
Substituting the values in choice A:
1.2 = √1.5 = 1.2247 Approximately equal.
1.2 = (1.5)^2 - 1 = 1.25 Approximately equal.
Choice B.
-1.2 = √-1.5 which is imaginary so NOT this one.
Choice C
-1.2 = √1.5 = -1.2247
-1.2 = (1.5)^2 - 1 = 1.25 NO.
Choice D
We have the non real value √-1.5 again so NOT this one.
Answer: Option A
A.(1.5,1.2)
Step-by-step explanation:
We have the following system of equations
[tex]y=\sqrt{x}[/tex]
[tex]y=x^2 -1[/tex]
the solution of the system will be all points that satisfy both equations at the same time
For (1.5,1.2)
[tex]y=\sqrt{1.5}=1.2[/tex]
[tex]y=(1.5)^2 -1=1.2[/tex]
Both equations are satisfied
Note that we can discard options B and D because the domain of the equation [tex]y =\sqrt{x}[/tex] does not include the negative numbers.
We can discard option C because the range of the function [tex]y =\sqrt{x}[/tex] does not include the negative numbers.
Finally the answer is the option A
Saloman was told the written paper on his science experiment should express measurements in liters.
Units of Capacity
Metric System Units Customary System Units
1 liter
0.26 gallon
1 liter
1.05 quarts
1 liter
4.22 cups
Which shows how to calculate the number of liters he used if he used 5 cups of water?
divide 5 by 4.22
multiply 5 by 4.22
divide 5 by 1.05
multiply 5 by 1.05
Final answer:
To find the liters for 5 cups of water, divide 5 by 4.22, according to the conversion rate obtained from the given table.
Explanation:
To calculate the number of liters used if Saloman used 5 cups of water, we need to determine how many cups are in a liter. According to the unit conversion provided, 1 liter is equivalent to approximately 4.22 cups. To find the number of liters from the number of cups, we should divide the total cups by the number of cups per liter. Therefore, to find the liters for 5 cups, we divide 5 by 4.22.
The calculation is: 5 cups ÷ 4.22 cups/liter = number of liters.
F(x)=x^2+3x+2 is shifted 2 units left.the result is g(x). What is g(x)?
Answer:
Either A or B.
Step-by-step explanation:
When shifting to the left you are adding to x.
Example: x^2 shifted to the left by 3. (x+3)^2
For this case we have that, by definition of horizontal translation of functions we have to:
We assume h> 0:
To graph[tex]y = f (x-h),[/tex] the graph moves, h units to the right.
To graph[tex]y = f (x + h)[/tex], the graph moves, h units to the left.
If we have the following function:
[tex]f (x) = x ^ 2 + 3x + 2[/tex]and move 2 units to the left, then:
[tex]f (x + 2) = g (x) = (x + 2) ^ 2 + 3 (x + 2) +2[/tex]
ANswer:
Option B
(3x^2-5x-7x^4)-(-2x^3+6x^4-5x^2)
Answer:
-13x^4+2x^3+8x^2-5x
Step-by-step explanation:
(3x^2-5x-7x^4)-(-2x^3+6x^4-5x^2)
= 3x^2-5x-7x^4+2x^3-6x^4+5x^2
= -13x^4+2x^3+8x^2-5x
Answer:
-x(13x³ - 2x² - 8x + 5)
Step-by-step explanation:
1. Distribute the negative to the numbers inside the parenthesis. Remember that two negatives multiplied will make a positive, and a negative and a positive will become a negative.
3x² - 5x - 7x^4 + 2x³ - 6x^4 + 5x²
2. Combine like terms. Remember that only numbers with the same number and exponents can be combined.
3x² - 5x - 7x^4 + 2x³ - 6x^4 + 5x²
↓
8x² - 5x - 7x^4 + 2x³ - 6x^4
↓
8x² - 5x - 13x^4 + 2x³
3. Rewrite the answer in descending order of powers.
-13x^4 + 2x³ + 8x² - 5x
4. Simplify The equation. The terms all have x in common, so we will take that out first. The smallest amount of x's any term has is one (-5x only has one x), so the most we can take out is one x. We will do this by lowering the power of every x by one.
x(-13x³ + 2x² + 8x - 5)
5. Since 13 and 5 are prime and do not go into 2 or 8 we will not be simplifying the coefficients. However, the last thing we can do is take out a negative.
-x(13x³ - 2x² - 8x + 5)
He has 2yards of the string .He cut 5 /8 yards of the string for his project how much left
For this case we must subtract:
[tex]2- \frac {5} {8} =\\\frac {8 * 2-5} {8} =\\\frac {16-5} {8} =\\\frac {11} {8}[/tex]
Thus, you have [tex]\frac {11} {8}[/tex]of string, after you have cut[tex]\frac {5} {8}[/tex] of it.
If we convert to a mixed number we have to:
[tex]\frac {11} {8} = 1 \frac {3} {8}[/tex]
Answer:
He has [tex]1 \frac {3} {8}[/tex] of string.
a^3b^-4/a^2b^3a^-5 write without rational notation and move all terms to numerator
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{a^3b^{-4}}{a^2b^3a^{-5}}\implies \cfrac{a^3}{1}\cdot b^{-4}\cdot \cfrac{1}{a^2}\cdot \cfrac{1}{b^3}\cdot \cfrac{1}{a^{-5}}\implies a^3\cdot b^{-4}\cdot a^{-2}\cdot b^{-3}\cdot a^5 \\\\\\ a^3a^5a^{-2}b^{-4}b^{-3}\implies a^{3+5-2}b^{-4-3}\implies a^6b^{-7}[/tex]
How do you convert 2/11 into a decimal ?
Answer:
you would divide the two numbers. 2 divided by 11 is 0.18
Answer:
0.181818182 or rounded is 0.18
Step-by-step explanation:
to turn any fraction into a decimal you always do numerator divided by denominator
Select the statements that are true for the graph
The vertex is (-2, 4)-
The vertex is (2,4)
The graph has a minimum
The graph has a maximum
The graph has a y-intercept of -8
Answer:
The graph has a minimum.
Step-by-step explanation:
The top answer choice would also be a genuine statement if that negative symbol was removed from outside the 4. Second, whenever A is positive, the parabola opens up with a minimum value.
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
A triangle has vertex A at (0, 0), vertex B at (2, 5), and vertex C at 1
(4, 5). Which side of the triangle has the greatest slope?
0
Check the picture below.
One can use two-dimensional objects to build three-dimensional objects?
True or False?
Answer:
TRUE
Step-by-step explanation:
How many dimensions does a plane have?
O A. One
O B. Three
O C. Two
O D. Zero
Answer is C. Two
Answer:
C: Two dimensions
Step-by-step explanation:
Yes: a plane has two dimensions; think of a plane as being defined by the x- and y-axes, which intersect at a point in the plane.
A plane have two dimensions.
What is plane?A plane is a flat, two-dimensional surface that prolongs infinitely far. A plane is a two-dimensional analogue that could consist of a point, a line and three-dimensional space.
A plane is a flat, two-dimensional surface that extends indefinitely. It has two dimensions because every point in the plane can be described by a linear combination of two independent vectors.
Hence, a plane have two dimensions.
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I would like to check my answer! Have I done this correctly ? :)
Answer:
Yes you are right.
The answer is .45 or 45/100 which reduces to 9/20.
Step-by-step explanation:
[tex]\frac{4x}{15}=\frac{3}{25}[/tex]
Your first step is to cross multiply:
[tex]15(3)=25(4x)[/tex]
Simplify both sides:
[tex]45=100x[/tex] You got this! You go!
Divide both sides by 100:
[tex]\frac{45}{100}=x[/tex]
You wrote 45/100 as .45 which is correct!
Nice.
Which graph represents the solution set of the inequality x+2 greater than or equal to 6
Answer:
4 ≤ x
4
●→
Step-by-step explanation:
There is no illustration, it looks something like this.
Simplify negative 5 minus the square root of negative 44
Answer:
Simplification of [tex]-5-\sqrt{-44}[/tex] is:
[tex]-5-2i\sqrt{11}[/tex]
Step-by-step explanation:
We are given a expression:
[tex]-5-\sqrt{-44}[/tex]
We have to simplify the given expression.
We know that:
[tex]\sqrt{-1}=i[/tex]
[tex]-5-\sqrt{-44}\\\\=-5-\sqrt{-4\times 11}\\ \\=-5-\sqrt{-1\times 2^2\times 11}\\ \\=-5-2i\sqrt{11}[/tex]
Hence, simplification of [tex]-5-\sqrt{-44}[/tex] is:
[tex]-5-2i\sqrt{11}[/tex]
in the diagram below what is the approximate length of the minor arc DE
Answer:
C. 52 cm
Step-by-step explanation:
A full circle has a degree measure of 360 degrees.
Minor arc DE is intercepted by a central angle of 120 degrees.
120 degrees is 1/3 of 360 degrees, so the length of minor arc DE is 1/3 of the circumference of the circle.
length of minor arc DE = (120/360) * 2 * pi * r
length of minor arc DE = (1/3) * 2 * 3.14 * 25 cm
length of minor arc DE = 52.3333... cm
Answer:
the correct answer is 52.
Step-by-step explanation:
I just got it correct.
In a certain card game you draw one card off a standard deck of 52 cards. If you draw a spade you get paid $12, if you draw a red Ace you get paid $20, and if you draw a red Queen you get paid $38. If you draw anything else, you get paid nothing. What should this game cost if it is to be a fair game? Use fractions in your work and then calculate the answer as a decimal rounded to 4 decimal places.
Step-by-step explanation:
In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades. That leaves 35 cards for everything else.
For the game to be fair, the cost must equal the expected value. The expected value is the sum of each outcome times its probability.
C = (12) (13/52) + (20) (2/52) + (38) (2/52) + (0) (35/52)
C = 68/13
C ≈ 5.2308
How to solve this 336+x/5=85
Answer:
x = -1255
Step-by-step explanation:
336+x/5=85
Subtract 336 from each side
336-336 +x/5=85-336
x/5 =-251
Multiply each side by 5
x/5 * 5 = -251 *5
x = -1255
Given the functions f(x) = 7x + 13 and g(x) = x + 2, which of the following functions represents f[g(x)] correctly? (2 points)
Answer:
The value of f[ g(x) ] = 7x + 27
Step-by-step explanation:
It is given that, f( x ) = 7x + 13 and g( x ) = x + 2
To find the value of f(g(x))
g(x) = x + 2 and 7x + 13 (given)
Let g(x) = x + 2
f [ g(x) ] = 7(x + 2) + 13 [ substitute the value of g(x) in f(x) ]
= 7x + 14 + 13
= 7x + 27
Therefore the value of f[ g(x) ] = 7x + 27
How do you do number 1?
Whenever I tried to answer it, I always get fraction. help me.
Answer:
The pairs are (13,15) and (-15,-13).
Step-by-step explanation:
If n is an odd integer, the very next odd integer will be n+2.
n+1 is even (so we aren't using this number)
The sum of the squares of (n) and (n+2) is 394.
This means
(n)^2+(n+2)^2=394
n^2+(n+2)(n+2)=394
n^2+n^2+4n+4=394 since (a+b)(a+b)=a^2+2ab+b^2
Combine like terms:
2n^2+4n+4=394
Subtract 394 on both sides:
2n^2+4n-390=0
Divide both sides by 2:
n^2+2n-195=0
Now we need to find two numbers that multiply to be -195 and add up to be 2.
15 and -13 since 15(-13)=-195 and 15+(-13)=2
So the factored form is
(n+15)(n-13)=0
This means we have n+15=0 and n-13=0 to solve.
n+15=0
Subtract 15 on both sides:
n=-15
n-13=0
Add 13 on both sides:
n=13
So if n=13 , then n+2=15.
If n=-15, then n+2=-13.
Let's check both results
(n,n+2)=(13,15)
13^2+15^2=169+225=394. So (13,15) looks good!
(n,n+2)=(-15,-13)
(-15)^2+(-13)^2=225+169=394. So (-15,-13) looks good!
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y=2x^2+4x-3
Answer:
Step-by-step explanation:
write this expression : f(x) = a(x-h)²+k
when the axis of symmetry is the line : x =h and the vertex A(h,k)
y=2x²+4x-3
y = 2(x²+2x - 3/2)
y=2((x²+2x+1) -1 -3/2)
y = 2((x+1)² - 5/2)
y = 2(x+1)² -5.....vertex form x= -1 the axis of symmetry and A(-1,-5)the vertex
Answer:
The equation of the axis of symmetry is x = -1.
The coordinates of the vertex are (-1, -5).
Step-by-step explanation:
y = 2x^2 + 4x - 3
y = 2(x^2 + 2x) - 3
y = 2[ (x + 1)^2 - 1] - 3
y = 2(x + 1)^2 - 5.
The equation of the axis of symmetry is x = -1.
The coordinates of the vertex are (-1, -5)
Angela has a marbles, Brian has twice as many marbles as Angela, Caden has three times as many marbles as Brian, and Daryl has five times the number of marbles Caden has. If in total Angela, Brian, Caden and Daryl have 78 marbles, what is the value of a?
Answer:
2
Step-by-step explanation:
Angela has a marbles.
Brian has twice as many as Angela, so Brain has 2a.
Caden has three times as many as Brain, so Caden has 3(2a)=6a.
Daryl has five times the number of marbles as Caden, so Daryl has 5(6a)=30a.
We are given that these 4 people together have 78 marbles.
Angela's + Brain's + Caden's + Daryl's =78
a + 2a + 6a + 30a =78
Combine the like terms:
39a=78
Divide both sides by 39:
a=78/39
a=2
Solve for f:
_
35
- f = 4
Answer:
f=31
Step-by-step explanation:
35-f=4
-35 -35
-f=-31
*-1 *-1
f=31
[tex]\large \textnormal{F=31}[/tex], is the correct answer.
[tex]\large \textnormal{First, subtract by 35 from both sides of the equation.}[/tex]
[tex]\displaystyle 35-f-35=4-35[/tex]
[tex]\large \textnormal{Solve.}[/tex]
[tex]\displaystyle -f=-31[/tex]
[tex]\large \textnormal{Then you divide by -1 from both sides of the equation.}[/tex]
[tex]\displaystyle \frac{-f}{-1}=\frac{-31}{-1}[/tex]
[tex]\large \textnormal{Solve to find the answer.}[/tex]
[tex]\displaystyle -31\div-1=31[/tex]
[tex]\large \boxed{f=31}\checkmark[/tex]
Hope this helps!
I got this question that says to Complete the table for the given rule. and that is y=5x and it says (the chart has only numbers under y so you have to find what number x is)
What number is x for 4 and 2
X Y
0 5
0 4
0 2
Answer:
X Y
1 5
4/5 4
2/5 2
Step-by-step explanation:
y=5x
We we know y we need to solve for x
X Y
5
4
2
Let y =5
5 = 5x
Divide by 5
5/5 =5x/5
1=x
Let y =4
4 = 5x
Divide by 5
4/5 =5x/5
4/5=x
Let y =2
2 = 5x
Divide by 5
2/5 =5x/5
2/5=x
X Y
1 5
4/5 4
2/5 2
Answer:
x=0.8 if y=4, x=0.4 if y=2
Step-by-step explanation:
Rearrange the equation to get:
5x= 4 and
5x= 2
Divide equations by 5 to get:
x=0.8
x=0.4
Subtract h + 3 from 6h + 1.
Enter your answer in the box.
Answer:
5h -2
Step-by-step explanation:
(6h + 1) - (h+3)
= 6h + 1 - h -3
= 5h -2
6h +1 - h+3
Subtract like terms:
6h - h = 5h
1-3 = -2
The answer becomes 5h-2
Gas costs $6 per gallon and diesel costs $8 per gallon. You have at most $85 to spend on fuel. You must purchase at least 12 gallons of gas for your car to run for the week. Let x be the amount of gas purchased and y be the amount of diesel purchased. Which of the following is a possible solution?
Answer:
(12,1.625)
Step-by-step explanation:
According to the given statement:
Cost of gas per gallon = $6
Cost of diesel per gallon = $8
Cost of x gallon gas = 6x
Cost of y gallon diesel = 8y
You have at most $85 to spend on fuel
Therefore the equation we get is:
6x+8y≤85
You must purchase at least 12 gallons of gas for your car
x≥12
Plot the graph and you get possible solutions:
(12,1.625)..
-3(8/9)÷66.9[9(-8.9+9/5).01]
i neeeed help or il fail the 6weeks
The answer of -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] is 0.06237948089
Step-by-step explanation:
To solve this problem -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] we must start with
1. Solve this bracket [9 (-8.9 + 9/5) .01] at first
2. Multiply the answer of the bracket by 66.9
3. Multiply -3(8/9) and divide the answer by the product of the previous
step
In [9 (-8.9 + 9/5) .01]
∵ (-8.9 + 9/5) = (-8.9 + 1.8) = -7.1
∴ [9 (-8.9 + 9/5) .01] = [9 (-7.1).01]
∵ 9(-7.1)(.01) = -0.639
∴ [9 (-8.9 + 9/5) .01] = -0.639
∵ 66.9 [-0.639] = -42.7491
∵ [tex]-3(\frac{8}{9})=\frac{-8}{3}[/tex]
∴ -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] = [tex]\frac{-8}{3}[/tex] ÷ -42.7491
∴ -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] = 0.06237948089
The answer of -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] is 0.06237948089
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for the level 3 course, examination hours cost twice as much as workshop hours and workshop hours cost twice as much as lecture hours. how id the lectures cost per hour? Total cost level 3 =$528
Answer:
The lectures cost is $7.33 per hour
Step-by-step explanation:
* Lets explain how to solve the problem
- For the level 3 course the examination hours cost twice as much
as workshop hours
- The workshop hours cost twice as much as lecture hours
- There are examination hours , workshop hours and lecture hours
- There are 3 hr for examination, 24 hr for workshops and 12 hr
for lectures
* Let the cost of the lecture hours is $x per hour
∴ The cost of the lecture hours is x per hour
∵ The cost of workshop hours is twice the cost of lecture hours
∴ The cost of the workshop hours is 2(x) = 2x per hour
∵ The cost of examination hours is twice the cost of workshop hours
∵ The cost of the workshop hours is 2x
∴ The cost of examination hours is 2(2x) = 4x per hour
- The cost of the level 3 is the sum of the costs of the lecture hours,
workshop hours and examination hours
∵ There is 12 hours for lectures
∵ There is 24 hours for workshops
∵ There is 3 hours for examination
∵ The total cost of level 3 = 12(x) + 24(2x) + 3(4x)
∴ The total cost of level 3 = 12 x + 48 x + 12 x
∵ The total cost of level 3 = $528
∴ 12 x + 48 x + 12 x = 528
∴ 72 x = 528 ⇒ divide both sides by 72
∴ x = 7.33
∵ x is the cost of the lecture hours per hour
∴ The lectures cost is $7.33 per hour
x - 3(x – 7) = 4(x – 7) – 2x
Answer:
x = 12.25
Step-by-step explanation:
Given
x - 3(x - 7) = 4(x - 7) - 2x ← distribute parenthesis on both sides
x - 3x + 21 = 4x - 28 - 2x ← simplify both sides
- 2x + 21 = 2x - 28 ( subtract 2x from both sides )
- 4x + 21 = - 28 ( subtract 21 from both sides )
- 4x = - 49 ( divide both sides by - 4 )
x = [tex]\frac{49}{4}[/tex] = 12.25
Answer: x=12.25
Step-by-step explanation: First, multiply the numbers into the parentheses. You will get:
X -3x +21 = 4x -28 -2x
Combine like terms.
-2x +21 =2x -28
Isolate x by adding 2x to each side.
21 =4x -28
Add 28 to each side to get x by itself.
49=4x
Divide by 4.
X =12.25
Here's another coaster that will help you think about the effect of a factor's exponent!
Once again, make the coaster cross at x = 500 after an initial rise and fall.
• This time, make your track more realistic: make the coaster come in smoothly at x = 1000 instead
of just falling and suddenly stopping!
y = Flax(x – 1000)
Answer: y=-ax(x-500)(x-1000)^2
Step-by-step explanation:
The behavior of the x-intercept of a graph is given by the multiplicity of the zero
The required polynomial for the coaster is, y = -a·x·(x - 500)·(x - 1000)²
Reason:
The question relates to the introduction of characteristics to the graph of a polynomial through knowledge of the effect of parameters of a polynomial
Known parameter:
Parent function is, y = a·x·(x - 1000)
The polynomial crosses the x-axis when (x - 500) is a factor of the polynomial, therefore, we have;
y = a·x·(x - 500)·(x - 1000)
Given that the graph is to initially rise, the leading coefficient is negative, therefore, we have;
y = -a·x·(x - 500)·(x - 1000)
For the polynomial to come in smoothly to stop at y = 0, when x = 1,000 we have that a turning point of the polynomial will be located at x = 1,000, this is given by introduction of a bump on the x-axis at x = 1,000 with a factor of (x - 1,000)²
Therefore, the required polynomial is y = -a·x·(x - 500)·(x - 1000)²
The height of the above polynomial is progressively smaller as x tends towards 1,000, given that the factors, (x - 500), and (x - 1,000), becomes smaller.
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Passing through (-2,1 ) and perpendicular to
4x + 7y + 3 = 0.
Answer:
7x - 4y + 18 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
========================================
Let
[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]
========================================
We have the equation of a line in a general form (Ax + By + C = 0)
Convert it to the slope-intercept form:
[tex]4x+7y+3=0[/tex] subtract 7y from both sides
[tex]4x+3=-7y[/tex] divide both sides by (-7)
[tex]-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}[/tex]
We have the equation:
[tex]y=\dfrac{7}{4}x+b[/tex]
Put the coordinates of the point (-2, 1) to the equation, and solve for b :
[tex]1=\dfrac{7}{4}(-2)+b[/tex]
[tex]1=-\dfrac{7}{2}+b[/tex] multiply both sides by 2
[tex]2=-7+2b[/tex] add 7 to both sides
[tex]9=2b[/tex] divide both sides by 2
[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]
Finally:
[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] - slope-intercept form
Convert to the general form:
[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] multiply both sides by 4
[tex]4y=7x+18[/tex] subtract 4y from both sides
[tex]0=7x-4y+18[/tex]