In order to find the equation of the line, first let's calculate its slope m using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the given points (x1, y1) = (-4, -4) and (x2, y2) = (3, 1), we have:
[tex]m=\frac{1-(-4)}{3-(-4)}=\frac{1+4}{3+4}=\frac{5}{7}[/tex]Now, to find the equation, let's use the slope-intercept form and calculate the value of b using a given point:
[tex]\begin{gathered} y=mx+b \\ (3,1): \\ 1=\frac{5}{7}\cdot3+b \\ 1=\frac{15}{7}+b \\ b=1-\frac{15}{7} \\ b=-\frac{8}{7} \end{gathered}[/tex]Therefore the equation is y = (5/7)x - 8/7
