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 formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For parallel lines in a trapezoid, the non - parallel sides have different slopes and the parallel sides have the same slope.

Step2: Analyze slope of parallel lines

In a trapezoid, the parallel sides have the same slope. If $WXYZ$ is a trapezoid, assume $WZ$ and $XY$ are parallel. So line $WZ$ has the same slope as line $XY$.

Step3: Analyze individual slopes

Let's assume we find the slopes of each line using two points on the line. For line $YX$, if we consider two points on it and calculate the slope, and do the same for line $ZY$. By visual inspection or calculation, we can see that line $YX$ has a positive slope and line $ZY$ has a negative slope, so line $YX$ has a greater slope than line $ZY$.

Step4: Analyze y - intercepts

The y - intercept is the value of $y$ when $x = 0$. By looking at the graph, we can see that line $ZW$ and line $YZ$ do not have the same y - intercept. Also, line $XY$ has a greater y - intercept than line $XW$. And line $XW$ has a positive slope and line $YZ$ has a negative slope, so line $XW$ does not have a lesser slope than line $YZ$.

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 $XW$. (Note: the last correct option was not exactly in the given list but based on the analysis of y - intercepts, the correct statements about slopes and y - intercepts among the given options are the first two). So the correct options from the list are:
Line $WZ$ has the same slope as line $XY$.
Line $YX$ has a greater slope than line $ZY$.