To find the equation of the line, as a first step we are going to calculate the slope of the line with the following expression:
Points given: (-4, -9) and (3, -2)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-(-9)}{3-(-4)} \\ m=\frac{7}{7}=1 \end{gathered}[/tex]Slope intercept form of a line is:
[tex]y=mx+b[/tex]But to get that expression, we are going to use the slope-point form:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y+9=1(x+4) \\ y=x+4-9 \\ y=x-5\text{ -> Slope-intercept form} \end{gathered}[/tex]