To derive the equation y = mx for a line through the origin based on a graph, we need to determine the slope (m) of the line.
The slope of a line is defined as the change in y divided by the change in x between any two points on the line. Since the line passes through the origin (0, 0), we can choose any point on the line and the coordinates of that point will be (x, y).
Let's consider two points on the line: point A (x1, y1) and the origin (0, 0). The change in y between these two points is y1 - 0 = y1, and the change in x is x1 - 0 = x1.
Therefore, the slope (m) can be calculated as:
m = (change in y) / (change in x)
= y1 / x1
Since the line passes through the origin, any point (x1, y1) on the line must satisfy the equation y1 = m * x1. Substituting the above expression for m, we can rewrite the equation as:
y1 = (y1 / x1) * x1
Simplifying gives:
y1 = y1
This equation shows that for any point (x1, y1) on the line, y equals y. Thus, the equation y = mx holds for a line passing through the origin.
use the graph to derive the equation y=mx for a line through the origin.
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