Question

brainy.com write a linear equation in slope intercept form with the given information. passes through (-2,-11) and is perpendicular to y=-(1/4)x+2

Answer 1

Hello :)

Slope intercept form: y = mx+b

Perpendicular: forms a right angle (90°)

We are asked to write the linear equation (written in slope intercept form) that passes through (-2,-11) and is perpendicular to $y=-(\frac{1}{4} )x+2$

to do this we need to find the perpendicular line using the point.

Step 1: use the point slope formula: $y-y_1=m (x-x_1)$ to find the line perpendicular to  $y=-(\frac{1}{4} )x+2$

m=4; we got 4 because we were supposed to find the negative reciprocal of the slope of the original line by multiplying -(1/4) by (-1).

$x_1:-2\\y_1:-11$

$y-(-11)=4(x-2)\\y+11=4(x-2)\\y+11=4x-8\\ -11 -11\\\\ y=4x-3$

y=4x-3

we can check this by seeing that when we graph it, the line passes through (-2,-11) , and it is also perpendicular to $y=-(\frac{1}{4} )x+2$

*use desmos*