Relationship A has a lesser rate than Relationship B. This table represents Relationship B.
Hours worked 2 4 5 8
Amount paid ($) 36.50 73 91.25 146
Which equation could represent Relationship A?
Hours worked is represented by x, and amount paid is represented by y.
Select each correct answer.
Responses
y = 18x
y, = 18, x
y = 18.3x
y, = 18.3, x
y = 18.6x
y, = 18.6, x
y = 18.1x
The correct equation that represents Relationship A would be:
y = 18x
To determine which equation could represent Relationship A, we can use the given information about Relationship B.
Relationship B has a rate where the amount paid doubles when the hours worked double. This indicates a direct proportionality between the hours worked and the amount paid.
Let's calculate the rate for Relationship B by dividing the amount paid by the hours worked:
For the first pair (2 hours, $36.50):
Rate = 36.50 / 2 = 18.25
For the second pair (4 hours, $73):
Rate = 73 / 4 = 18.25
For the third pair (5 hours, $91.25):
Rate = 91.25 / 5 = 18.25
For the fourth pair (8 hours, $146):
Rate = 146 / 8 = 18.25
Since the rate is consistent at 18.25, we can say that Relationship A also has a rate of 18.25.
Now, we can check each equation to see if it matches the rate of 18.25:
1. y = 18x: This equation represents a rate of 18, not 18.25. Therefore, it does not match the given information.
2. y = 18.3x: This equation represents a rate of 18.3, not 18.25. Therefore, it does not match the given information.
3. y = 18.6x: This equation represents a rate of 18.6, not 18.25. Therefore, it does not match the given information.
4. y = 18.1x: This equation represents a rate of 18.1, not 18.25. Therefore, it does not match the given information.
None of the provided equations match the rate of 18.25, so none of them represent Relationship A.
To find the equation representing Relationship A, we need to analyze the given data for Relationship B and determine the pattern between the hours worked and the amount paid.
By examining the table, we can observe that as the hours worked increase, the amount paid also increases. This indicates that there is a linear relationship between the variables. To determine the equation, we need to find the rate of increase, known as the slope.
In this case, we can calculate the slope by selecting any two points from the table and applying the formula:
slope (m) = (change in y) / (change in x)
Let's choose the first two points (2, 36.50) and (4, 73):
slope (m) = (73 - 36.50) / (4 - 2)
= 36.50 / 2
= 18.25
The slope is 18.25, which means for each hour worked, the amount paid increases by $18.25.
Now that we have the slope, we can write the equation representing Relationship A using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept (which we don't know yet).
So, the equation representing Relationship A would be:
y = 18.25x + b
Since we don't have the specific y-intercept, we can't determine the exact equation. However, we can eliminate the options that don't match the slope.
Analyzing the options provided:
1. y = 18x: This option represents a slope of 18, which is not the same as the slope calculated for Relationship B (18.25). Hence, this option is incorrect.
2. y = 18.3x: This option represents a slope of 18.3, which is not the same as the slope calculated for Relationship B (18.25). Hence, this option is incorrect.
3. y = 18.6x: This option represents a slope of 18.6, which is also different from the slope calculated for Relationship B (18.25). Hence, this option is incorrect.
4. y = 18.1x: This option represents a slope of 18.1, which is still different from the slope calculated for Relationship B (18.25). Hence, this option is also incorrect.
Therefore, there isn't an option provided that matches the slope of Relationship B, so we can't determine the exact equation for Relationship A based on the given options.