Please help me in this

Question

What is the equation of a line that is perpendicular to the line y = –14x – 1 and passes through the point (3, 7)?

A. y = –4x + 19

B. y = 4x – 5

C. y = 14x + 254

D. y = –4x + 31

Answer 1

Hi Jessica T

Per your correction in the comments above the line is

y = (-1/4)x -1

with slope, m = (-1/4)

A line perpendicular to the one above would have a slope that is the numerical inverse with the opposite sign

the numerical inverse with the opposite sign for (-1/4) is 4

y = 4x + b

Use the coordinates given to solve for b

7 = 4(3) + b

7 = 12 + b

7 - 12 = b

-5 = b

Finally

y = 4x - 5

You can graph both lines at Desmos.com to confirm that they are perpendicular to each other.

Thanks so much for updating the information in the comments and I hope this helps

Answer 2

Hey!

First, we need to know that perpendicular slopes have negative reciprocals. This means flip the slope (m) and change the sign to get the perpendicular slope! In your case, I think you meant y= (-1/4)x - 1.

So the reciprocal of m (-1/4) is positive 4/1, or just 4 for simplicity's sake.

We also are given a point (3,7). We know that to get a new equation using only the slope and a given point, we use point-slope form:

y-y₁=m(x-x₁). where (x_1,y₁) is our point and m is our slope

Subbing everything we have, we get:

y-7=4(x-3)

y-7-4x-12

Using a bit of arithmetic, we should be able to figure out the answer choice from there!

Edit: as mentioned earlier, you can also plug in the point given for (x,y). The new equations will often have a different y-intercept!