A line passes through the point (–2, 4), and its y-intercept is (0, –6). What is the equation of the line that is perpendicular to the first line and passes through the point (5, –4)?

Question

anonymous · Answer

Okay this one is a bit harder than the last one. Can you work out the gradient? Then we can put it in the formula I told you in your last question.

anonymous · Answer

okayy is it 1/5x-3

anonymous · Answer

The gradient is a number, it shouldn't have any Xs in it or symbols (subtraction). To calculate the gradient, it is the change in y divided by the change in x. From (-2,4) to (0,-6) the line moves across two and down 10.

-10/2 = -5. The gradient is -5.

Now we want the normal (perpendicular line) to this which is the negative reciprocal of the gradient, so -(1/(-5))=1/5.

(y-y1)=m(x-x1)

y-(-4)=1/5(x-5)
y+4=1/5x-1
y=1/5x-5

You were so close, but I think you missed a negative sign on one of the last steps :) Great work!

anonymous · Answer

Oh okay. Thanxx so much <3

anonymous · Answer

No problem, happy to help! Let me know if you get stuck with any others.

Tom

P.S. I've just realised I forgot to delete my first paragraph:

"The gradient is a number, it shouldn't have any Xs in it or symbols (subtraction). To calculate the gradient, it is the change in y divided by the change in x. From (-2,4) to (0,-6) the line moves across two and down 10."

You can ignore that! I thought you were saying the gradient was 1/5x-3 so I started off saying why you were wrong, but then as I went to solve it realised that you were saying it was the equation of the line so it was my mistake, not yours.