Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
To derive the equation y=mx for a line through the origin, we first need to find the slope of the line. From the graph, we can see that the line passes through the origin, meaning that the y-intercept is 0.
The slope of the line can be calculated by taking the change in y divided by the change in x for two points on the line. Let's choose the points (1, 2) and (2, 4) from the graph.
Change in y: 4 - 2 = 2
Change in x: 2 - 1 = 1
Slope (m) = 2/1 = 2
Now that we have determined the slope of the line, we can write the equation as y = 2x. Since the slope is 2, we can simplify the numerical coefficient to get y = 2x.