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 [tex]y=-(\frac{1}{4} )x+2[/tex]
to do this we need to find the perpendicular line using the point.
Step 1: use the point slope formula: [tex]y-y_1=m (x-x_1)[/tex] to find the line perpendicular to [tex]y=-(\frac{1}{4} )x+2[/tex]
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).
[tex]x_1:-2\\y_1:-11[/tex]
[tex]y-(-11)=4(x-2)\\y+11=4(x-2)\\y+11=4x-8\\ -11 -11\\\\ y=4x-3[/tex]
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 [tex]y=-(\frac{1}{4} )x+2[/tex]
*use desmos*
