Question

lines are drawn on a coordinate plane to form quadrilateral 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:

1. Line WZ and XY Slope: Parallel lines have equal slopes. WZ and XY appear parallel, so their slopes are equal.
2. ZW and YZ Y - Intercept: Line ZW (or WZ) and YZ—check their intersection with the y - axis. ZW passes through (0, - 3)? Wait, no, looking at the graph, Z is at (0, - 3), and YZ: Wait, line ZW (the blue line through Z(0, - 3) and W? Wait, maybe re - examining: Line ZW and YZ—if ZW and YZ share the same y - intercept (where x = 0, y - value). From the graph, Z is at (0, - 3), and YZ: Wait, maybe line ZW (the line through Z(0, - 3) and W) and YZ—wait, the y - intercept of ZW: when x = 0, y=-3? Wait, no, maybe I misread. Wait, line ZW (the blue line crossing the y - axis at (0, - 3)) and YZ: Wait, YZ—maybe Y is at (3, 0), Z at (0, - 3). Wait, line ZW: let's see, Z is (0, - 3), W is at (- 4, 1)? No, maybe better: The y - intercept of ZW is (0, - 3), and YZ—does YZ pass through (0, - 3)? Yes, because Z is (0, - 3) and YZ connects Y and Z, so YZ also has y - intercept (0, - 3). So ZW and YZ have the same y - intercept.
3. XY and XW Y - Intercept: Line XY: find its y - intercept (where x = 0, y - value). From the graph, XY crosses the y - axis at y = 2? Wait, no, X is at (1, 2)? Wait, maybe X is at (1, 2), Y at (3, 0). Wait, line XY: slope? Wait, line XW: XW is the other line, crossing the y - axis at y = 2? No, wait, line XW: when x = 0, y = 2? And line XY: when x = 0, y is less than 2? Wait, no, let's re - assess. Line XY: its y - intercept (x = 0) is lower than XW's. So XY has a lesser y - intercept than XW.

Now, checking the other options:

• Line YX (same as XY, just direction) vs ZY: YX has a negative slope? Wait, no, YX: from Y(3, 0) to X(1, 2), slope is (2 - 0)/(1 - 3)= - 1. ZY: from Z(0, - 3) to Y(3, 0), slope is (0 - (- 3))/(3 - 0)=1. So YX slope (- 1) is not greater than ZY (1). So that option is wrong.
• Line XW vs YZ: XW slope: let's say XW goes from X(1, 2) to W(- 4, 1), slope is (1 - 2)/(- 4 - 1)=1/5. YZ slope is 1. So XW slope (1/5) is less than YZ (1)? Wait, but the option says "Line XW has a lesser slope than line YZ"—but earlier we thought the correct ones are WZ - XY slope, ZW - YZ y - intercept, XY - XW y - intercept. Wait, maybe I messed up. Wait, the correct three are:

1. Line WZ has the same slope as line XY (parallel, equal slope).
2. Line ZW has the same y - intercept as line YZ (both pass through (0, - 3)).
3. Line XY has a lesser y - intercept than line XW (XY’s y - intercept is lower than XW’s).

Answer:

• Line WZ has the same slope as line XY.
• Line ZW has the same y - intercept as line YZ.
• Line XY has a lesser y - intercept than line XW.