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
1
1
2
2
−2
negative 2
The slope of the line is -1 or negative 1.
To find the slope of a line, we can use the formula:
slope = (change in y-coordinate) / (change in x-coordinate)
Looking at the given line, we can see that it passes through the points (0, 0), (2, -2), (4, -4), and (6, -6).
Using these points, we can calculate the change in y-coordinate and change in x-coordinate:
Change in y-coordinate: -6 - 0 = -6
Change in x-coordinate: 6 - 0 = 6
Now, we can calculate the slope:
slope = (-6) / (6) = -1
Therefore, the slope of the line is -1.
To find the slope of a line, you can use the formula:
slope = (change in y)/(change in x)
The slope of a line represents its steepness or inclination.
In this case, we can see that the line passes through the points (0,0), (2,-2), (4,-4), and (6,-6).
To calculate the change in y, we subtract the y-coordinates of two points on the line. Let's take the points (0,0) and (2,-2).
Change in y = -2 - 0 = -2
To calculate the change in x, we subtract the x-coordinates of the same two points.
Change in x = 2 - 0 = 2
Now, we can substitute these values into the slope formula:
slope = (-2) / 2 = -1
The slope of the line is -1.
Therefore, the correct answer is: negative 1.