someone help me ASAP

Question

Write the equation of a line perpendicular to 2x -7y =3 and passes through the points (-4,5) 

 

Group of answer choices

7x+2y=18

y=(-7/2)x-9

2x-7y=-18

y=(7/2)x+19

Answer 1

Here is an alternative way to do it which I like.

For a perpendicular line change 2x - 7y to 7x + 2y and just say 7x + 2y = C

Now put in the point (-4,5) to find C

7(-4) + 2(5) = C

C = -18

7x + 2y = -18

In slope intercept form that would be y = (-7/2)x - 9

Answer 2

Hi Amira H.

It is the second choice

y= (-7/2)x - 9

Solve 2x - 7y = 3 for y

This puts in in slope intercept form

y = mx + b

y = (2/7)x - 3/7

m = 2/7

The perpendicular line would have an inverse slope with the opposite sign, negative in this so

m = (-7/2)

y = (-7/2)x + b

Use the coordinates (-4, 5) given to solve for b

5 = (-7/2)(-4) + b

5 = 14 +

5 - 14 = b

-9 = b

and finally

y = (-7/2)x - 9

You can graph both lines on the same grid at desmos.com to see that they are perpendicular