Question

Find the equation of a line perpendicular to y= 3x + 7 that passes through the point (9,-7).

Answer 1

Okay so the gradient of the perpendicular line is -1/3 and then from there u have to solve for the y intercept. Substitute in 9 and -7 where -7 is y and 9 is x. The equation is y=-1/3x-4 :)

Answer 2

Answer:

$y=-\frac{1}{3}x-4$

Step-by-step explanation:

To find the slope perpendicular to this, take the negative reciprocal of the slope. Basically, invert both the fraction and the negative/positive so that 3 becomes -1/3.

Now, using the new slope and the given point, we can find the y-intercept. Plug the 3 known variables into the equation:

$y=mx+b\\-7=(-\frac{1}{3})(9)+b$

Then, solve for b:

$-7=-3+b\\-4=b\\b=-4$

Finally, with both the slope and the y-intercept, you can write the equation of the line:

$y=-\frac{1}{3}x-4$