Slope as Unit Rate Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 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 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 1 comma 2 right parenthesis, left parenthesis 2 comma 4 right parenthesis, left parenthesis 3 comma 6 right parenthesis, and left parenthesis 4 comma 8 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 3 comma 0 right parenthesis, and left parenthesis 3 comma 6 right parenthesis. The base is labeled as 3, and the perpendicular height on the right is labeled as 6. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 3 comma 6 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 2.
Use similar triangles to determine the slope of the line.
To determine the slope of the line, we can use the formula:
slope = change in y / change in x
In this case, the change in y between the two triangles is 6 and the change in x is 3.
Therefore, the slope of the line is 6/3 = 2.
Slope as Unit Rate Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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 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
.
To determine the slope of the line, we can use the formula:
slope = change in y / change in x
In this case, the change in y between the two triangles is 2 and the change in x is 4.
Therefore, the slope of the line is 2/4 = 1/2.
Slope as Unit Rate Quick Check
1 of 51 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 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 $0.10 per ounce.
Canned peas cost $0.10 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 $3.00 per ounce
To determine the unit rate of the proportional relationship, we need to find the cost per ounce.
Looking at the graph, we can see that when the number of ounces is 8, the cost is $0.80.
Therefore, the unit rate of the proportional relationship is $0.80 per ounce.
it doesn't give me the answer 0.80
I apologize for the confusion. Let's recheck the data and find the correct answer:
From the graph, we can see that when the number of ounces is 8, the cost is $0.80.
To find the unit rate, we divide the cost by the number of ounces:
$0.80 / 8 = $0.10
Therefore, the unit rate of the proportional relationship is $0.10 per ounce.
Slope as Unit Rate Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows two graphs depicting cost of gasoline per gallon in dollars in store A and B. The first graph shows cost of gasoline per gallon in dollars in store A. The horizontal axis shows gallons ranging from 0 to 20 in increments of 5. The vertical axis shows the cost in dollars ranging from 0 to 70 in increments of 10. 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. The second graph shows cost of gasoline per gallon in dollars in store B. The horizontal axis shows gallons ranging from 0 to 10 in increments of 2. The vertical axis shows the cost in dollars ranging from 0 to 30 in increments of 2. Three data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma 14 right parenthesis, and left parenthesis 8 comma 28 right parenthesis. A line connects all the data points.
The proportional relationship between the cost of gasoline and the number of gallons of gasoline from Store A and Store B are displayed in the graphs. Use the graphs to interpret the store that has the cheaper cost of gasoline per gallon.
(1 point)
Responses
Store B has the cheaper gasoline. The cost of gasoline at Store A is $5 per gallon.
Store B has the cheaper gasoline. The cost of gasoline at Store A is $5 per gallon.
Store A has the cheaper gasoline. The cost of gasoline is $0.25 per gallon.
Store A has the cheaper gasoline. The cost of gasoline is $0.25 per gallon.
Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.
Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.
Store B has the cheaper gasoline. The cost of gasoline at Store A is $100 per gallon
To determine which store has the cheaper cost of gasoline per gallon, compare the slopes of the two lines on the graphs.
Looking at Store A, as the number of gallons increases by 5 (from 0 to 5), the cost increases by $20.
Therefore, the slope of the line for Store A is $20 / 5 = $4 per gallon.
Looking at Store B, as the number of gallons increases by 4 (from 0 to 4), the cost increases by $14.
Therefore, the slope of the line for Store B is $14 / 4 = $3.50 per gallon.
Since $3.50 < $4, Store B has the cheaper cost of gasoline per gallon.