find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph

Answer 1

To find the equation of the line, we need to determine the value of m using the given graph. Since the relationship shown in the graph is proportional, it means that for every change in x, there is a constant change in y.

Since the line passes through the origin (0, 0), we can conclude that when x = 0, y = 0. Then, the slope of the line (m) can be found by calculating the change in y divided by the change in x for any other point on the line.

Let's choose another point on the line, such as (2, 4):

m = (change in y) / (change in x)
= (4 - 0) / (2 - 0)
= 4/2
= 2

Now, we have the slope (m = 2), and we can write the equation of the line using the slope-intercept form of a linear equation (y = mx + b), where b is the y-intercept but since the line passes through the origin, b = 0.

Therefore, the equation of the line is:
y = 2x