Question

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

Answer 1

`y=-(1)/(3)x-4`

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=(-(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=-(1)/(3)x-4`

Answer 2

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 :)