Slope as Unit Rate Quick Check
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Question
Use the image to answer the question.
An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through four plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 4 comma negative 4 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis. The base is labeled as 2, and the perpendicular height on the left is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 2 comma negative 6 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The base is labeled as 4, and the perpendicular height on the left is labeled as 4.
What is the slope of the line?
(1 point)
Responses
−2
negative 2
2
2
1
1
−1
The slope of the line is −1.
To find the slope of a line, we can use the formula:
slope = (change in y) / (change in x)
Looking at the line passing through the points (0,0), (2,-2), (4,-4), and (6,-6), we can calculate the change in y and change in x.
For the change in y, we look at the y-coordinate of the final point minus the y-coordinate of the initial point:
change in y = -6 - 0 = -6
For the change in x, we look at the x-coordinate of the final point minus the x-coordinate of the initial point:
change in x = 6 - 0 = 6
Now we can plug these values into the slope formula:
slope = (-6) / 6 = -1
So the slope of the line is -1.