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=33x
y equals Start Fraction 3 over 3 End Fraction x
y=x
y equals x
y=8x
y equals 8 x
y=3x
y equals 3x
To derive the equation y=mx for a line through the origin using a graph, you can follow these steps:
1. Identify the y-intercept of the line, which is the point where the line intersects the y-axis. Since the line passes through the origin (0,0), the y-intercept is 0.
2. Determine the slope of the line. The slope is the change in y divided by the change in x between any two points on the line. In this case, we can choose the point (1, y) on the line, where y represents the y-coordinate we are trying to find. By comparing this point to the origin (0,0), we can see that the change in y is y - 0 = y, and the change in x is 1 - 0 = 1. Therefore, the slope of the line is y/1 = y.
3. Combine the y-intercept and slope to form the equation y=mx. Since the y-intercept is 0, the equation becomes y = 0x + y, which simplifies to y = y.
From the given options, the equation y = 3x satisfies the requirement of a line through the origin. The numerical coefficient, 3, is already simplified.
To derive the equation for a line through the origin using the given graph, we can observe the slope (m) of the line.
Looking at the graph, we can see that the line passes through the origin (0,0) and has a slope of 3, which means that for every unit increase in x, y increases by 3.
Therefore, the equation y = mx, where m is the slope, can be written as:
y = 3x
So, the equation for the line through the origin is y = 3x.