Slope as Unit Rate Quick Check
5 of 55 of 5 Items
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
−1
negative 1
−2
negative 2
1
1
2
2
The slope of the line can be found using the formula: slope = (change in y)/(change in x).
From the given points, we can see that the change in y is -2 and the change in x is 2.
Therefore, the slope of the line is: slope = (-2)/(2) = -1.
So, the correct answer is -1.
To find the slope of a line, we can use the formula:
slope = change in y / change in x
From the given image, we can see that the line passes through the points (0, 0), (2, -2), (4, -4), and (6, -6).
First, let's calculate the change in y:
Change in y = final y-coordinate - initial y-coordinate
For the points (0, 0) and (2, -2):
Change in y = -2 - 0 = -2
For the points (2, -2) and (4, -4):
Change in y = -4 - (-2) = -4 + 2 = -2
For the points (4, -4) and (6, -6):
Change in y = -6 - (-4) = -6 + 4 = -2
Next, let's calculate the change in x:
Change in x = final x-coordinate - initial x-coordinate
For the points (0, 0) and (2, -2):
Change in x = 2 - 0 = 2
For the points (2, -2) and (4, -4):
Change in x = 4 - 2 = 2
For the points (4, -4) and (6, -6):
Change in x = 6 - 4 = 2
Now, let's calculate the slope:
Slope = change in y / change in x
For the given line, the change in y = -2 + (-2) + (-2) = -6
And the change in x = 2 + 2 + 2 = 6
Slope = -6/6 = -1
Therefore, the slope of the line is -1 (or negative 1).