We have to find the equation of the line that passes through the points (-1, -8) and (3, 4).
We can calculate the slope m as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-(-8)}{3-(-1)}=\frac{4+8}{3+1}=\frac{12}{4}=3[/tex]Then, we can write the equation in slope-point form as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-(-8)=3(x-(-1)) \\ y+8=3(x+1) \end{gathered}[/tex]In this form, the equation does not match any of the options, but if we use the other point (3,4) to write the equation, we get another version:
[tex]y-4=3(x-3)[/tex]This match the first option.
Answer: y - 4 = 3(x - 3)
