Question

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

Answer 1

Answer:

y=1/3x - 2

Step-by-step 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

$\frac{1}{3} =\frac{y--1}{x-3}$

cross-multiply

$\frac{1}{3} =\frac{y+1}{x-3} \\\\\\1(x-3)=3(y+1)\\\\\\x-3=3y+3\\\\-3-3=3y-x\\\\-6=3y-x$

Divide every term by 3

$-2=y-\frac{1}{3} x\\\\\\-2+\frac{1}{3} x=y$

The line is

$y=\frac{1}{3} x-2$