Question

Determine the equation of the line that passes through the point (8, -20) and is perpendicular to the line y = 1/3x + 5. Enter the slope intercept form

Answer 1

Answer:

$y=-3x+4$

For an equation to be perpendicular, the slope must be the negative reciprocal of the other equation.

Given that the slope of the line y = 1/3x + 5 is 1/3,

$\frac{1}{3}\Rightarrow(-1)(\frac{1}{\frac{1}{3}})=-3$

Now we have a slope of -3, we will use the following equation to find the y-intercept of the equation:

$y=mx+b$

Using the point (8, -20)

$y=mx+b\Rightarrow-20=(-3)(8)+b$$-20=-24+b\Rightarrow b=-20+24$$b=4$

Now we got the y-intercept 4. Substituting this to the equation

$y=mx+b$

And we will get:

$y=-3x+4$

Therefore, the equation of the line that passes through the point (8, -20) and is perpendicular to the line y = 1/3x + 5 is:

$y=-3x+4$