Question

Which line has a slope of frac{1}{3} and goes through (3, -1)?

Answer 1

y=1/3x - 2

Explanation:

The question asks for the equation of a line with a slope of 1/3 and passes through point (3,-1)

The equation for the line in the slope intercept form is written as y=mx+c where m is the gradient and c is the y-intercept

But you know m=Δy/Δx where Δx =x-3 and Δy=y--1

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

cross-multiply

`(1)/(3) =(y+1)/(x-3) \\\\\\1(x-3)=3(y+1)\\\\\\x-3=3y+3\\\\-3-3=3y-x\\\\-6=3y-x\\`

Divide every term by 3

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

The line is

`y=(1)/(3) x-2`