Chelsea G.

asked • 03/29/20# Find an equation of the line that (a) has the same y-intercept as the line y + 4 x − 10 = 0 and (b) is parallel to the line 1 x + 7 y = 6 . Write your answer in the form y = m x + b .

Find an equation of the line that (a) has the same y-intercept as the line y+4x−10=0 and (b) is parallel to the line 1x+7y=6.Write your answer in the form y=mx+b.

where y=____x+_____

## 3 Answers By Expert Tutors

Miss Keegan P. answered • 03/29/20

Experienced Tutor for both Math and Science

Hello!

First you will want to get both of equations into slope-intercept form. That way, you can easily determine the y-intercept of the first equation and the slope of the second equation.

When 2 lines have the same slope, that means they will be parallel.

y+4x-10=0 ; add 10 to each side

y+4x=10 ; subtract 4x from each side

y = -4x + 10 ; y-intercept = 10

1x + 7y = 6 ; subtract 1x from each side

7y = -1x + 6 ; divide both sides by 7

y = -1/7 x + 6/7 ; slope = -1/7

So, a line with the same y-intercept as the first, and same slope (parallel) as the second would have the equation:

y = -1/7x + 10

Chelsea G.

thank you so much!03/29/20

Reese K. answered • 03/29/20

Yale Undergrad Tutor for Math, Science, Writing, Test Prep, and Bridge

Hi!

a) The first thing you want to do is rearrange this into standard slope-intercept form (y=mx+b). So by adding 10 to each side, and subtracting 4x from each side, you get:

y = -4x + 10

So your y-intercept is going to be 10.

b) Here you want to do the same, but it's slightly trickier. If you subtract 1x from both sides, and then divide by 7, you get:

7y = 6 - 1x

y = 6/7 - 1/7x which is the same as y = -1/7x + 6/7.

So for the two lines to be parallel, they must have the same slope. So your slope here is (-1/7)x.

Putting a) and b) together:

You take the y-intercept from a) and the slope from b) to get y = -1/7x + 10! Good question!

James M. answered • 03/29/20

Math tutoring from K-to-Jr High and SAT, GED Preparation

To solve this problem you must recall:

Parallel lines have the same slopes

And the y-intercept of a line in slope intercept form (y = mx+b) is the value of b.

To be parallel to the x+7y =6 indicates the slope must be -1/7 because the line given is y= -1/7x+6

y=-1/7

To have the same y-intercept as y +4x-10= 0 the value is 10 because this line is y = y = -4x +10

Y=-1/7X +10

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Miss Keegan P.

So welcome! Let me know if I can help with anything else.03/29/20