Answer:
Option 2
Step-by-step explanation:
First, find the slope of the line of the graph using the points given as (5, -3) and (13, -9):
[tex] slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 -(-3)}{13 - 5} = \frac{-6}{8} = -\frac{3}{4} [/tex]
Any of the triangle in the options given, whose opp side has the same slope value of -¾, is the triangle we are looking for.
Option 1: slope between the points (0, 2) and (3, -2).
[tex] slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 2}{3 - 0} = \frac{-4}{3} [/tex]
Option 2: slope between the point (-7, 6) and (-3, 3).
[tex] slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 6}{-3 -(-7)} = \frac{-3}{4} [/tex]
Option 2 has the same slope as the one given in the graph. This is the answer.
Option 3: slope between the points (5, -1) and (2, -5).
[tex] slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 -(-1)}{2 - 5} = \frac{-4}{-3} = \frac{4}{3} [/tex]
Option 4: slope between the points (2, -7) and (6, -4).
[tex] slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -(-7)}{6 - 2} = \frac{3}{4} = \frac{3}{4} [/tex]
The answer is Option 2
