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
[tex]\frac{1}{3} =\frac{y--1}{x-3}[/tex]
cross-multiply
[tex]\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\\[/tex]
Divide every term by 3
[tex]-2=y-\frac{1}{3} x\\\\\\-2+\frac{1}{3} x=y[/tex]
The line is
[tex]y=\frac{1}{3} x-2[/tex]
