Question

four lines are drawn on a coordinate plane to form trapezoid wxyz. which statements are true about the lines? select three options. line wz has the same slope as line xy. line yx has a greater slope than line zy. line xw has a lesser slope than line yz. line zw has the same y - intercept as line yz. line xy has a lesser y - intercept than line xw.

Explanation:

Step1: Recall slope formula

The slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. The $y$-intercept is the value of $y$ when $x = 0$.

Step2: Analyze parallel - lines and slopes

In a trapezoid, one pair of opposite sides is parallel. Parallel lines have the same slope. If $WXYZ$ is a trapezoid, assume $WZ\parallel XY$. So, line $WZ$ has the same slope as line $XY$.

Step3: Compare slopes visually

By observing the graph, we can see that line $YX$ has a positive slope and line $ZY$ has a negative slope. A positive slope is greater than a negative slope, so line $YX$ has a greater slope than line $ZY$.

Step4: Analyze $y$-intercepts

The $y$-intercept of a line is the point where the line crosses the $y$-axis. By observing the graph, we can see that the $y$-intercept of line $XY$ is greater than the $y$-intercept of line $XW$.

Answer:

Line $WZ$ has the same slope as line $XY$, Line $YX$ has a greater slope than line $ZY$, Line $XY$ has a greater $y$-intercept than line $XW$. So the correct options are:

• Line $WZ$ has the same slope as line $XY$.
• Line $YX$ has a greater slope than line $ZY$.
• Line $XY$ has a greater $y$-intercept than line $XW$.