If one line passes through the points (x₁, y₁) and (x₂, y), the slope of the line can be calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}...(1)[/tex]Additionally, the equation can be expressed in point-slope form as:
[tex]y-y_2=m(x-x_2)...(2)[/tex]From the problem, we identify:
[tex]\begin{gathered} (x_1,y_1)=(-7,-3) \\ \\ (x_2,y_2)=(-2,4) \end{gathered}[/tex]Then, we calculate the slope of the line using (1):
[tex]m=\frac{4-(-3)}{-2-(-7)}=\frac{4+3}{-2+7}=\frac{7}{5}[/tex]Finally, we find the equation of the line using (2):
[tex]\therefore y-4=\frac{7}{5}(x+2)[/tex]