we are given a line and we are asked to determine a graph of a line that is parallel to the given line. the graph of the parallel line is the following:
Now we will determine the slope of the given line using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph we choose the following points:
[tex]\begin{gathered} (x_1,y_1)=(-9,0) \\ (x_2,y_2)=(0,-6) \end{gathered}[/tex]replacing in the formula we get:
[tex]m=\frac{-6}{0-(-9)}=-\frac{6}{9}=-\frac{2}{3}[/tex]therefore, the slope of the given line is -2/3.
To determine the slope of the line we draw we use the following points:
[tex]\begin{gathered} (x_1,y_1)=(-3,0) \\ (x_2,y_2)=(0,-2) \end{gathered}[/tex]replacing in the formula for the slope:
[tex]m=\frac{-2-0}{0-(-3)}=-\frac{2}{3}[/tex]therefore, the slope of the line is -2/3, as expected the two slopes are equal due to the fact that the lines are parallel.
