From the given graph, the coordinates of the four points are A(-4,-2), B(4,4), C(0,-3) and D(4,0).
Find the equation of the line joining A and B using the two point formula.
[tex]\begin{gathered} y-(-2)=\frac{4-(-2)}{4-(-4)}(x_{}-(-4)) \\ y+2=\frac{6}{8}(x+4) \\ y=\frac{3}{4}x+\frac{3}{4}\cdot4-2 \\ y=\frac{3}{4}x+1 \end{gathered}[/tex]Find the equation of the line joining C and D using the two point formula.
[tex]\begin{gathered} (y-(-3))=\frac{0-(-3)}{4-0}(x-0) \\ y+3=\frac{3}{4}x \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]The equation of the line is in the form y = mx+c, where m is the slope and c is the y-intercept.
Here:
Slope of the line joining A and B = 3/4
Slope of the line joining C and D = 3/4
So, the lines are parallel because their slopes are equal.