In order to find the equation that represents this line, let's use two points of the line in the slope-intercept form of the linear equation:
[tex]y=mx+b[/tex]
Using the points (-2, 1) and (4, 6), we have:
[tex]\begin{gathered} y=mx+b \\ (-2,1)\colon \\ 1=-2m+b \\ (4,6)\colon \\ 6=4m+b \end{gathered}[/tex]
Multiplying the first equation by 2 and adding it with the second equation, we have:
[tex]\begin{gathered} 2=-4m+2b \\ 2+6=-4m+2b+(4m+b) \\ 8=3b \\ b=\frac{8}{3} \\ \\ 1=-2m+\frac{8}{3} \\ 2m=\frac{8}{3}-1 \\ 2m=\frac{5}{3} \\ m=\frac{5}{6} \end{gathered}[/tex]
So our equation is:
[tex]y=\frac{5}{6}x+\frac{8}{3}[/tex]
