The proportional relationship is shown on the graph. Derive the equation of the line y=mx through the origin.

Answer 1

In a proportional relationship, the equation of the line through the origin is given by y = mx, where m is the slope of the line.

To derive the equation of the line y = mx from the graph, we need to find the slope (m) of the line.

The slope of a line can be found by taking any two points on the line and using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

In this case, since the line passes through the origin, the y-intercept is 0, and any point on the line can be used to find the slope.

Let's take two points on the line from the graph. Let's say (x1, y1) = (2, 4) and (x2, y2) = (4, 8).

Using the formula for slope, we have:
m = (y2 - y1)/(x2 - x1)
= (8 - 4)/(4 - 2)
= 4/2
= 2

So the slope (m) of the line is 2.

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