Question

What is the equation of the line in slope-intercept form that passes through the point (3, –5) and is perpendicular to y = –3x + 4?

Answer 1

`y=1/3x-6`

Explanation:

`y=-3x+4` has a slope of `color(purple)(-3)` (It is in slope-intercept form)
therefore
any line perpendicular to it has a slope of `-1/(color(purple)(-3))=color(green)(1/3)`

Starting with the slope-point form, with a slope of `color(green)(1/3)` and a point `(color(red)(3),color(blue)(-5))`
we have
`color(white)("XXX")y-(color(blue)(-5))=color(green)(1/3)(x-color(red)(3))`

`color(white)("XXX")y+5=color(green)(1/3)(x)-1`

`color(white)("XXX")y=color(green)(1/3)xcolor(brown)(-6)`

which is the "slope-intercept" form with slope `color(green)(1/3)` and y-intercept `color(brown)(""(-6))`