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)
NO
the answer to number 5 is -3 btw
To derive the equation of the proportional relationship through the origin, we need to determine the ratio between the quantities and the costs on the graph.
Looking at the points plotted on the graph, we can see that the cost increases by a constant ratio of 9 each time the quantity increases by 1. This means that for every increase of 1 in quantity, the cost increases by 9.
Since the relationship is proportional, we can write the equation in the form y = kx, where y represents the cost, x represents the quantity, and k is the constant proportionality factor.
In this case, since the relationship goes through the origin, the y-intercept is 0. Therefore, the equation can be simplified to y = kx.
Using the points on the graph, we can calculate the value of k by selecting any two points. Let's use the points (1, 9) and (2, 18):
Using the equation y = kx, we can substitute the values for these points:
9 = k(1)
18 = k(2)
Solving for k, we can divide the second equation by the first equation:
18/9 = k(2)/k(1)
2 = 2k/k
2 = k
Therefore, the equation of the proportional relationship through the origin is y = 2x.
The equation of the proportional relationship through the origin can be derived by finding the slope of the line.
The slope of a line is determined by the change in the y-values over the change in the x-values.
In this case, the change in the y-values is 9, 18, 27, and 36, and the corresponding change in the x-values is 1, 2, 3, and 4.
Therefore, the slope of the line is 9/1 = 18/2 = 27/3 = 36/4 = 9.
The equation of the proportional relationship is y = 9x.
To derive the equation of the proportional relationship through the origin, we can use the slope-intercept form of a linear equation, which is y = mx.
In this case, y represents the cost and x represents the quantity. The equation needs to go through the origin, which means the y-intercept is 0. Therefore, the equation can be written as y = mx + 0, which simplifies to y = mx.
To find the value of m, we can use the slope of the line on the graph, which represents the cost per quantity. Looking at the graph, we can see that for each increase in quantity by 1, the cost increases by 9.
Therefore, the slope or the cost per quantity is 9. And the equation of the proportional relationship through the origin is y = 9x.