Question

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

point slope form, thanks :) ​

Answer 1

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

Explanation:

Perpendicular lines have opposite reciprocal slopes, meaning that if you had
`(4)/(3)`, the opposite would change the sign:
`-(4)/(3)`, and the reciprocal would flip the fraction:
`(-3)/(4)`

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

• Opposite:
  `(1)/(3)` Change the sign
• Reciprocal:
  `(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.