Question

Find the equation for the line that passes through the point (4, -2), and that is parallel to the line with the equation y = 1/3x-8/3

Answer 1

`y=(1)/(3)x-(10)/(3)`

Explanation:

Parallel lines have the same slope, but different y-intercepts, thus:

`y=(1)/(3)x+b\\\\-2=(1)/(3)(4)+b\\ \\-2=(4)/(3)+b\\ \\-(10)/(3)=b`

This means our parallel equation that passes through (4,-2) is
`y=(1)/(3)x-(10)/(3)`.