Note: For questions 17–19, your teacher will grade your responses to ensure you receive proper credit for your answers.
Which triangle can be used to find the slope of the line shown? Explain your answer.
A line and two right triangles are shown on the coordinate plane.
The line passes through the points left-parenthesis negative 2 comma 0 right-parenthesis and left-parenthesis 0 comma 2 right-parenthesis. A small triangle is labeled A. Its hypotenuse lies on the line. It has vertices at left-parenthesis negative 5 comma negative 3 right-parenthesis, left-parenthesis negative 3 comma negative 3 right-parenthesis and left-parenthesis negative 3 comma negative 1 right-parenthesis. A large triangle is labeled B. Its hypotenuse lies on the line. It has vertices at left-parenthesis 2 comma 0 right-parenthesis, left-parenthesis 5 comma 0 right-parenthesis and left-parenthesis 3 comma 5 right-parenthesis.
(3 points)
To find the slope of the line, we can use triangle B. Triangle B has vertices at points (2,0), (5,0), and (3,5). By calculating the rise (difference in y-coordinates) and the run (difference in x-coordinates) between two of the vertices, we can find the slope of the line passing through those points. The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using points (2,0) and (3,5) from triangle B, we get:
m = (5 - 0) / (3 - 2)
m = 5 / 1
m = 5
Therefore, the slope of the line passing through the points (2,0) and (3,5) is 5, which can be calculated using triangle B.