Question

write the equation of a line perpendicular to y =-1/ 8x that passes through point (-12, - 4)

point slope form, thanks :) ​

Answer 1

Answer:

$y+4=3(x+12)$

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, meaning that if you had $\frac{4}{3}$, the opposite would change the sign: $-\frac{4}{3}$, and the reciprocal would flip the fraction: $\frac{-3}{4}$

We can find the slope of the line perpendicular to the line $y=-\frac{1}{3}x-8$ by finding the opposite reciprocal of -1/3 (slope is the coefficient of x).

• Opposite: $\frac{1}{3}$                                                               Change the sign
• Reciprocal: $\frac{3}{1}=3$                                                      Flip the fraction

Now we have the slope of the line and a point that the line passes through. We are now able to use point-slope form.

Point-slope form:

• $y-y_1=m(x-x_1)$

Where $(x_1, \ y_1)$ are the coordinates of a point that the line passes through, and $m$ is the slope of the line.

Substitute (-12, -4) and m = 3 into the point-slope equation.

• $y-(-4)=3(x-(-12))$

Distribute the negative sign inside the parentheses.

• $y+4=3(x+12)$

This is the equation of the line perpendicular to y = -1/3x - 8 and that passes through point (-12, -4) in point-slope form.