Question

A line passes through the origin and has a slope of –3. What is the equation of the line that is perpendicular to the first line and passes through the point (3, 4)?

Answer 1

The given line has slope
`m=-3`. The slope of the line perpendicular to this line is
`-(1)/(m) =(1)/(3)`.

Its equation is
`y=(1)/(3) x+c`. Since this line passes through,
`(3,4)`,

`4=(1)/(3) (3)+c\\ c=3`

Thus the equation of the line in slope intercept form is
`y=(1)/(3) x+3`