To derive the equation y=mx for a line through the origin, we can use the slope-intercept form of a line: y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Since the line passes through the origin, we know that the y-intercept, b, is equal to zero. Therefore, the equation simplifies to y = mx.
To find the value of the slope, m, we can examine the graph. The slope is determined by the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
In this case, we can choose two convenient points on the line, such as (0, 0) (the origin) and (1, 2). The rise between these two points is 2 - 0 = 2, and the run is 1 - 0 = 1.
Therefore, the slope, m, is equal to the rise divided by the run:
m = (2 - 0) / (1 - 0)
m = 2/1
m = 2
Finally, substituting the value of m into the equation, we get y = 2x as the equation for the line through the origin.
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed
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