Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
(1 point)
Responses
y=8x
y equals 8 x
y=33x
y equals Start Fraction 3 over 3 End Fraction x
y=x
y equals x
y=3x
y=3x
To derive the equation y=mx for a line through the origin using the given graph, we need to find the value of the slope (m).
Looking at the graph, we can observe that the line passes through the origin (0,0), meaning the y-intercept is 0.
Now, we need to determine the slope. The slope of a line passing through the origin is equal to the change in y divided by the change in x between any two points on the line.
Taking two points from the graph, let's say (2,6) and (4,12), we can find the slope as follows:
m = (change in y) / (change in x)
= (12 - 6) / (4 - 2)
= 6 / 2
= 3
Thus, the equation of the line through the origin can be simplified to y = 3x, with the numerical coefficient (m) being 3.