The slope-intercept form of a linear equation is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
The slope m is
[tex]m=\frac{\Delta y}{\Delta x}=\frac{6-0}{0--12}[/tex][tex]m=\frac{1}{2}[/tex]And the y-intercept is found by using one of the points given and choosing a value of b that satisfies the equation.
Using the point (0,6) we get
[tex]6=\frac{1}{2}(0)+b[/tex][tex]\textcolor{#FF7968}{\therefore b=6}[/tex]Hence, we now have the slope-intercept form
[tex]\textcolor{#FF7968}{y=\frac{1}{2}x+6.}[/tex]