Slope as Unit Rate Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows Quadrant 1 of a coordinate plane. The x-axis is labeled Games and ranges from 0 to 7 in 1 unit increments. The y-axis is labeled points and ranges from 0 to 250 in increments of 50. The graph is titled Points per Game. A line connects four points plotted on the graph. The coordinates of the plotted points are left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma 90 right parenthesis, left parenthesis 5 comma 150 right parenthesis, and left parenthesis 7 comma 210 right parenthesis.
The graph displays the number of points scored and the number of basketball games played. Determine the average points per game.
(1 point)
An average of
points were scored per game.
To find the average points per game, we need to find the slope of the line connecting the four points on the graph.
The slope of a line can be found by using the formula:
slope = (change in y)/(change in x)
In this case, the change in y is the change in points and the change in x is the change in games.
Given the coordinates of the plotted points:
(0, 0)
(3, 90)
(5, 150)
(7, 210)
We can calculate the change in points and change in games as follows:
Change in points = 210 - 0 = 210
Change in games = 7 - 0 = 7
Now we can calculate the slope:
slope = (change in y)/(change in x) = 210/7 = 30
Therefore, the average points per game is 30.
Use the image to answer the question.
An illustration shows two graphs depicting cost per day in dollars for options A and B. The first graph shows cost per day in dollars for option A. The horizontal axis shows days ranging from 0 to 28 in increments of 7. The vertical axis shows the cost in dollars ranging from 0 to 70 in increments of 7. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 7 comma 21 right parenthesis, left parenthesis 14 comma 42 right parenthesis, and left parenthesis 21 comma 63 right parenthesis. A line connects all the data points. The second graph shows cost per day in dollars for option B. The horizontal axis shows days ranging from 0 to 20 in increments of 5. The vertical axis shows the cost in dollars ranging from 0 to 60 in increments of 20. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 5 comma 20 right parenthesis, left parenthesis 10 comma 40 right parenthesis, and left parenthesis 15 comma 60 right parenthesis. A line connects all the data points.
Two options for passes to ride public transportation are displayed in the graphs. Is Option A or Option B the better buy? Choose 1 for Option A and 2 for Option B.
(1 point)
is the better buy.
To determine which option is the better buy, we need to compare the slopes of the two lines.
For Option A, the coordinates of the plotted points are:
(0, 0)
(7, 21)
(14, 42)
(21, 63)
The change in cost for Option A is 63 - 0 = 63.
The change in days for Option A is 21 - 0 = 21.
Therefore, the slope for Option A is 63/21 = 3.
For Option B, the coordinates of the plotted points are:
(0, 0)
(5, 20)
(10, 40)
(15, 60)
The change in cost for Option B is 60 - 0 = 60.
The change in days for Option B is 15 - 0 = 15.
Therefore, the slope for Option B is 60/15 = 4.
Since the slope represents the cost per day, the lower the slope, the better buy.
Option A has a slope of 3, while Option B has a slope of 4.
Therefore, Option A is the better buy.
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 five 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 1 right parenthesis, left parenthesis 4 comma 2 right parenthesis, left parenthesis 6 comma 3 right parenthesis, and left parenthesis 8 comma 4 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 4 comma 0 right parenthesis, and left parenthesis 4 comma 2 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 4 comma 2 right parenthesis, left parenthesis 8 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2.
Use similar triangles to determine the slope of the line. Write your answer in fraction form.
(1 point)
The slope is
.
We can determine the slope of the line by comparing the change in y-coordinates to the change in x-coordinates between any two points on the line.
Let's consider two points on the line: (0, 0) and (4, 2).
The change in y-coordinates is 2 - 0 = 2.
The change in x-coordinates is 4 - 0 = 4.
Therefore, the slope between these two points is 2/4 = 1/2.
Since the line passes through multiple points, and we can observe from the image that all the triangles formed by the line have the same shape, we can conclude that the slope of the line remains constant.
Therefore, the slope of the line is 1/2.
Use the image to answer the question.
An illustration shows Quadrant 1 of a coordinate plane. The x-axis is labeled Ounces and ranges from 0 to 40 in 5 unit increments. The y-axis is labeled Cost in dollars and ranges from from 0.00 to 4.00 in increments of 0.50. The graph is titled Cost per Ounce. A line connects four points plotted on the graph. The coordinates of the plotted points are left parenthesis 0 comma 0 right parenthesis, left parenthesis 8 comma 0.80 right parenthesis, left parenthesis 15 comma 1.50 right parenthesis, and left parenthesis 30 comma 3.00 right parenthesis.
The graph displays the cost per ounce of canned peas. Use the graph to determine the unit rate of the proportional relationship.
(1 point)
Responses
Canned peas cost $3.00 per ounce.
Canned peas cost $3.00 per ounce.
Canned peas cost $30 per ounce.
Canned peas cost $30 per ounce.
Canned peas cost $10 per ounce.
Canned peas cost $10 per ounce.
Canned peas cost $0.10 per ounce.
To determine the unit rate of the proportional relationship, we need to find the cost of the canned peas per ounce.
Looking at the graph and the plotted points given, we can observe the following:
When there are 0 ounces of peas, the cost is $0.00.
When there are 8 ounces of peas, the cost is $0.80.
When there are 15 ounces of peas, the cost is $1.50.
When there are 30 ounces of peas, the cost is $3.00.
To find the unit rate, we need to divide the cost by the number of ounces. Let's take the last data point as an example:
Cost = $3.00
Ounces = 30
Unit Rate = Cost/Ounces = $3.00/30 = $0.10
Therefore, the unit rate of the proportional relationship is $0.10 per ounce.