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)
The equation of the proportional relationship through the origin can be derived from the graph as follows:
The graph shows that as the quantity of footballs increases by 1, the cost increases by 9. Therefore, the rate of change is constant and equal to 9.
Since the relationship is proportional and passes through the origin, the equation can be written in the form y = mx, where m represents the rate of change.
Thus, the equation of the proportional relationship is y = 9x.
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 3 comma 1 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 9 comma 3 right parenthesis.
Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
To find the equation of the line y = mx that describes the proportional relationship shown in the graph, we need to find the slope (m) of the line.
Using the points (3, 1) and (9, 3) that the line passes through, we can calculate the slope:
m = (change in y) / (change in x) = (3 - 1) / (9 - 3) = 2 / 6 = 1/3
So, the slope (m) of the line is 1/3.
Since the line passes through the origin, the equation becomes y = (1/3)x, where m = 1/3.
are u sure
Apologies for the confusion. Let's recalculate the slope and find the correct equation.
Using the points (3, 1) and (9, 3), we can calculate the slope as:
m = (change in y) / (change in x) = (3 - 1) / (9 - 3) = 2 / 6 = 1/3
So, the slope (m) of the line is 1/3.
Since the line passes through the origin, the equation becomes y = mx, where m = 1/3.
Therefore, the correct equation of the line y = mx that describes the proportional relationship shown in the graph is y = (1/3)x.
To derive the equation of the proportional relationship through the origin using the given graph, we can observe that the line segment connecting the points follows a linear pattern.
Let the equation of the proportional relationship be y = mx, where m represents the slope.
From the graph, we can see that at x = 0, y = 0. This represents the origin.
Using the two points on the line segment, (0,0) and (1,9), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (9 - 0) / (1 - 0)
m = 9 / 1
m = 9
Therefore, the equation of the proportional relationship through the origin is:
y = 9x
To derive the equation of the proportional relationship through the origin using the given graph, we can observe that the line segment connecting the points has a constant slope.
First, let's find the slope of the line segment.
We can choose any two points on the line segment to calculate the slope. Let's choose the points (0, 0) and (2, 18).
The slope formula is given by:
slope = (y2 - y1) / (x2 - x1)
Using the points (0, 0) and (2, 18), we can plug in the values:
slope = (18 - 0) / (2 - 0)
slope = 18/2
slope = 9
So, the slope of the line segment is 9.
Now, since the equation represents a proportional relationship through the origin, the equation can be written in the form y = kx, where k is the constant of proportionality.
Substituting the slope of 9 into the equation, we have:
y = 9x
Therefore, the equation of the proportional relationship depicted by the graph is y = 9x.