ANSWER:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]STEP-BY-STEP EXPLANATION:
The equation of the line in its slope and intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{ where m is the slope and b is y-intercept} \end{gathered}[/tex]The slope can be calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points (-1 , 1) and (5 , -3) :
[tex]m=\frac{-3-1}{5-(-1)}=\frac{-4}{5+1}=-\frac{4}{6}=-\frac{2}{3}[/tex]Now, we calculate the value of b, with the help of the slope and the point (-1,1)
[tex]\begin{gathered} 1=-\frac{2}{3}\cdot-1+b \\ b=1-\frac{2}{3} \\ b=\frac{1}{3} \end{gathered}[/tex]Therefore, the equation would be:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]
