Question

graph the function on the coordinate plane directly from the equation. the graph must include five points and four congruent right triangles drawn between the points. label all points with the correct ordered pairs. draw a line through the five points with arrowheads that extend beyond the grid edges. 14) $y = -\frac{5}{2}x$ coordinate plane grid

Explanation:

Step1: Choose x-values

Select x-values: -2, -1, 0, 1, 2 (easy to calculate y).

Step2: Calculate y for x=-2

Substitute \( x = -2 \) into \( y = -\frac{5}{2}x \):
\( y = -\frac{5}{2}(-2) = 5 \). Point: \( (-2, 5) \).

Step3: Calculate y for x=-1

Substitute \( x = -1 \):
\( y = -\frac{5}{2}(-1) = \frac{5}{2} = 2.5 \). Point: \( (-1, 2.5) \).

Step4: Calculate y for x=0

Substitute \( x = 0 \):
\( y = -\frac{5}{2}(0) = 0 \). Point: \( (0, 0) \).

Step5: Calculate y for x=1

Substitute \( x = 1 \):
\( y = -\frac{5}{2}(1) = -2.5 \). Point: \( (1, -2.5) \).

Step6: Calculate y for x=2

Substitute \( x = 2 \):
\( y = -\frac{5}{2}(2) = -5 \). Point: \( (2, -5) \).

Step7: Plot points & draw triangles

Plot \( (-2, 5) \), \( (-1, 2.5) \), \( (0, 0) \), \( (1, -2.5) \), \( (2, -5) \).
For congruent triangles: Between \( (-2,5) \) & \( (-1,2.5) \): horizontal change \( +1 \), vertical change \( -2.5 \) (slope \( -2.5 = -\frac{5}{2} \)). Repeat for other adjacent points (same horizontal/vertical changes, so triangles are congruent).

Step8: Draw the line

Draw a line through the points with arrowheads (extending beyond the grid).

Answer:

Points: \( (-2, 5) \), \( (-1, 2.5) \), \( (0, 0) \), \( (1, -2.5) \), \( (2, -5) \).
(Graph: Plot these points, draw congruent right triangles between adjacent points, then draw the line with arrowheads.)