Use the image to answer the question. The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin. (1 point)

Answer 1

To derive the equation of the line y=mx through the origin, we need to find the value of the slope (m).

Looking at the graph, we can see that the line passes through the origin, which means the y-intercept is zero (b = 0). Therefore, the equation of the line can be simplified to y = mx.

To find the slope, we can use the formula: m = (change in y) / (change in x).

Looking at the graph, we can see that as x increases by 2 units, y increases by 4 units. Therefore, the change in y is 4 and the change in x is 2.

Plugging these values into the slope formula, we get:
m = 4 / 2
m = 2

Therefore, the equation of the line y=mx through the origin is y = 2x.