We are to find the equation of the line joining the points
[tex](-3,-3),(12,2)[/tex]
The equation of a line is given as
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the given points we have
[tex]\begin{gathered} x_1=-3,x_2=12 \\ y_1=-3,y_2=2_{} \end{gathered}[/tex]
Therefore, the equation of the line is
[tex]\frac{y-(-3)}{x-(-3)}=\frac{2-(-3)}{12-(-2)}[/tex]
This gives
[tex]\frac{y+3}{x+3}=\frac{2+3}{12+3}[/tex]
Simplifying this we have
[tex]\begin{gathered} \frac{y+3}{x+3}=\frac{5}{15} \\ \frac{y+3}{x+3}=\frac{1}{3} \end{gathered}[/tex]
This further gives
[tex]\begin{gathered} 3(y+3)=x+3 \\ 3y+9=x+3 \\ 3y=x+3-9 \\ 3y=x-6 \end{gathered}[/tex]
Dividing both sides by 3 we get
[tex]\begin{gathered} y=\frac{1}{3}x-\frac{6}{3} \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]
Therefore, the equation is
[tex]y=\frac{1}{3}x-2[/tex]
