Question
page 14 of 15
Graphing Proportional Relationships 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 a graph labeled Football Cost. The horizontal axis is labeled Quantity and ranges from 0 to 5 in increments of 1. The vertical axis is labeled Cost and ranges from 0 to 39 in increments of 3. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 18 right parenthesis, left parenthesis 3 comma 27 right parenthesis, and left parenthesis 4 comma 36 right parenthesis.
The price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin.
(1 point)
Graphing Proportional Relationships 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 a graph labeled Football Cost. The horizontal axis is labeled Quantity and ranges from 0 to 5 in increments of 1. The vertical axis is labeled Cost and ranges from 0 to 39 in increments of 3. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 18 right parenthesis, left parenthesis 3 comma 27 right parenthesis, and left parenthesis 4 comma 36 right parenthesis.
The price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin.
(1 point)
Answers
GPT-4o mini
To derive the equation of the proportional relationship shown in the graph, we can use the information provided about the points plotted on the graph.
The points provided are:
- (0, 0)
- (1, 9)
- (2, 18)
- (3, 27)
- (4, 36)
In a proportional relationship, the equation can be expressed in the form \( y = kx \), where \( k \) is the constant of proportionality.
To find \( k \), we can use one of the points. For example, using the point (1, 9):
- When \( x = 1 \), \( y = 9 \).
Substituting these values into the equation:
\[ 9 = k(1) \]
So, \( k = 9 \).
Now, we have \( y = 9x \).
Thus, the equation of the proportional relationship is:
\[
y = 9x
\]
This means that for every football purchased (where \( x \) is the quantity), the cost (represented by \( y \)) is 9 times the quantity.
The points provided are:
- (0, 0)
- (1, 9)
- (2, 18)
- (3, 27)
- (4, 36)
In a proportional relationship, the equation can be expressed in the form \( y = kx \), where \( k \) is the constant of proportionality.
To find \( k \), we can use one of the points. For example, using the point (1, 9):
- When \( x = 1 \), \( y = 9 \).
Substituting these values into the equation:
\[ 9 = k(1) \]
So, \( k = 9 \).
Now, we have \( y = 9x \).
Thus, the equation of the proportional relationship is:
\[
y = 9x
\]
This means that for every football purchased (where \( x \) is the quantity), the cost (represented by \( y \)) is 9 times the quantity.