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

`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,

`(1)/(3)\Rightarrow(-1)((1)/((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`