Slope as Unit Rate Quick Check
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 $3.00 per ounce.
Canned peas cost $3.00 per ounce.
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.
The unit rate of the proportional relationship shown in the graph is $0.10 per ounce.
To determine the unit rate of the proportional relationship from the given graph, we need to find the slope of the line connecting the plotted points.
The slope of a line can be calculated using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
From the given coordinates:
Point A: (0, 0)
Point B: (8, 0.80)
Point C: (15, 1.50)
Point D: (30, 3.00)
Using the formula, let's calculate the slope between Point A and Point B:
slope1 = (0.80 - 0) / (8 - 0)
slope1 = 0.80 / 8
slope1 = 0.10
Let's calculate the slope between Point B and Point C:
slope2 = (1.50 - 0.80) / (15 - 8)
slope2 = 0.70 / 7
slope2 = 0.10
And finally, let's calculate the slope between Point C and Point D:
slope3 = (3.00 - 1.50) / (30 - 15)
slope3 = 1.50 / 15
slope3 = 0.10
From these calculations, we can see that the slope between any two points on the line is equal to 0.10.
Therefore, the unit rate of the proportional relationship is $0.10 per ounce.