Question

1. consider the graph of line m.

a. which pair of points can be used to draw a slope triangle for line m? choose all that apply.
a. (-8,4) and (-4,5)
b. (-8,4) and (0,6)
c. (-8,4) and (8,8)
d. (-4,5) and (0,6)
e. (0,6) and (8,8)
b. choose one correct pair of points from part (a). draw a slope triangle by using these points.
c. find the slope of line m.

Explanation:

Step1: Recall slope - triangle concept

Any two points on the line can be used to form a slope - triangle.

Step2: Check each option

• For option A: The points (-8,4) and (-4,5) lie on the line.
• For option B: The points (-8,4) and (0,6) lie on the line.
• For option C: The points (-8,4) and (8,8) lie on the line.
• For option D: The points (-4,5) and (0,6) lie on the line.
• For option E: The points (0,6) and (8,8) lie on the line.

So all options A, B, C, D, E are correct for part a.

Step3: Choose a pair for part b

Let's choose (-8,4) and (0,6)

Step4: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$

Step5: Calculate the slope for part c

Let $(x_1,y_1)=(-8,4)$ and $(x_2,y_2)=(0,6)$
$m=\frac{6 - 4}{0-(-8)}=\frac{2}{8}=\frac{1}{4}$

Answer:

a. A. (-8,4) and (-4,5), B. (-8,4) and (0,6), C. (-8,4) and (8,8), D. (-4,5) and (0,6), E. (0,6) and (8,8)
b. (Choose (-8,4) and (0,6) to draw a slope - triangle. In a graph, plot the two points, draw a horizontal line from (-8,4) and a vertical line from (0,6) to form a right - triangle)
c. $\frac{1}{4}$