Question

write an equation of the line perpendicular to the given line that contains P in point slope form? P (4,-4) y=1/3x+4

Answer 1

Answer: $y+4=-3(x-4)$

Step-by-step explanation:

- The equation of the line in point-slope form is:

$y-y_1=m(x-x_1)$

Where m is the slope and $(x_1,y_1)$ is a point of the line.

- The equation of the line $y=\frac{1}{3}x+4$ is written is slope-intercept form, where the slope is $\frac{1}{3}$.

- By definition, when two lines are perpendicular to each other, the slopes are the negative reciprocals. Therefore, the slope of the perpendicular line must be -3.

- Substitute the point P and the slope -3 into the equation in point-slope form, therefore, you obtain:

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