Graphing Proportional Relationships Practice Complete this assessment to review what you've learned. It will not count toward your grade. 3 of 53 of 5 Items Question Use the image to answer the question. Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph. (1 point)
Based on the given information, it is not possible to determine the equation of the line y=mx. More information such as the slope or coordinates of another point on the line is needed.
To find the equation of a line that describes a proportional relationship through the origin, we need to determine the slope of the line (m).
In the given graph, we can see that the line passes through the origin, which means the y-intercept (b) is 0.
The slope (m) of the line can be found by taking the ratio of the change in y-coordinate to the change in x-coordinate between any two points on the line.
Let's choose two points on the line. From the graph, we can see that as the x-coordinate increases by 1, the y-coordinate also increases by 1. We can choose the points (1, 1) and (2, 2) to calculate the slope.
The change in y = 2 - 1 = 1
The change in x = 2 - 1 = 1
So, the slope (m) = change in y / change in x = 1 / 1 = 1.
Therefore, the equation of the line y = mx through the origin is y = 1x, which can be simplified to y = x.
To find the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph, we need to determine the slope, m.
The slope, m, represents the rate of change (or the constant of proportionality) in a proportional relationship. It can be calculated by finding the ratio of the change in y-coordinates (vertical change) to the change in x-coordinates (horizontal change) between any two points on the line.
Since the line passes through the origin (0,0), we can choose any other point on the line to calculate the slope. Let's choose the point (1,3) as it is clearly shown on the graph.
The change in y-coordinates is given by y2 - y1 = 3 - 0 = 3.
The change in x-coordinates is given by x2 - x1 = 1 - 0 = 1.
Now, we can calculate the slope using the formula:
m = (change in y-coordinates) / (change in x-coordinates) = 3 / 1 = 3.
Therefore, the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph is:
y = 3x.