help me please help

Question

Look at each equation. Does the equation represent a line with slope 

m = 5,containing the point (3, 8)?Select Yes or No for each equation.

 

Yes or No 5x − y = 7

Yes or No x + 8y = 5

Yes or No 10x − 2y = 14

Answer 1

So to get our answer first we will solve the equation for y and then we will plug in the point given to see if that equation holds.

Given:

m = 5 point = (3,8)

A)5x - y = 7

so first we will move everything to the right side so we will subtract 5x from both sides

-y = 7 - 5x

Now we will divide both sides of the equation by -1

(-y/-1) = (7 - 5x)/(-1)

y = -7 + 5x

or anyway to write this

y = 5x - 7

Now we will take the point=(3,8) and plug it in the equation

x = 3, y = 8

y = 5x - 7

8 = 5(3) - 7

8 = 15 - 7

8 = 8 check

So for the first one the answer is YES

B) x + 8y = 5

so like the first one we will move everything to the right so subtract x from both sides

8y = 5 - x

Now divide everything by 8

y = (5/8) - (x/8)

since we have a common denominator an other way to write this is

y = (-x + 5)/(8)

Now if you compare this equation to y = mx + b you see that the slope of this equation is (-1/8) so we don't need to go any further but we will go another step and just prove this equation doesn't hold so we take the point = (3,8) and plug it in the equation

x = 3, y = 8

8 = (-3 + 5)/(8)

multiply the 8 on both sides and doing the subtraction you get

64 = 2 which is NOT true

so for the second one it is NO.

C)10x − 2y = 14

First we are gonna pull out a 2

2(5x - y) = 14

Then we divide the whole equation from 2

2(5x - y) / (2) = (14)/(2)

5x - y = 7

Now we move everything to the right side so we subtract 5x from both sides

-y = 7 - 5x

Next we divide the whole equation by -1

(-y/-1) = (7 - 5x)/(-1)

y = -7 + 5x

or an other way to write this is

y = 5x - 7

now we take the point = (3,8) and plug in the equation

8 = 5(3) - 7

8 = 15 - 7

8 = 8 check

so the answer to third question is YES

Answer 2

To answer this question, we must put each equation into y=mx+b form, and then plug in (3,8) as x and y values to determine if the equation is true.

1. 5x-y=7, to put into y=mx+b, add y and subtract 7 on each side.

y=5x-7 -----> This line has a slope of 5

8=5(3)-7

8=8 ---------> This line has the point (3,8) on it.

This logic can be applied to the other two problems.