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=3/3 x
y=3x
y=8x
y=x
The graph does not provide enough information to determine the slope of the line.
To derive the equation y = mx for a line through the origin using a graph, you need to look for the slope of the line. The slope, represented by m, is the coefficient of x in the equation.
In this case, looking at the given options, we can eliminate y = 8x and y = x because these lines do not pass through the origin (0,0). This leaves us with two options: y = 3/3 x and y = 3x.
To determine which one of these equations is correct, we need to look at the slope (m). In the equation y = 3/3 x, the numerical coefficient of x is 3/3, which simplifies to 1. So the slope for this equation is 1.
In the equation y = 3x, the numerical coefficient of x is already simplified, which is 3. So the slope for this equation is 3.
Since we are looking for the equation of a line through the origin, which means the y-intercept is 0, the correct equation is y = 3x.
To derive the equation y=mx for a line through the origin using the given graph, we need to find the slope of the line.
Looking at the graph, we can see that the line passes through the origin (0,0), which means the y-intercept is 0.
The slope of a line passing through the origin is given by the rise over the run. From the graph, we can see that for every 1 unit increase in x, there is a corresponding increase of 1 unit in y.
Therefore, the slope (m) is 1/1, or simply 1.
So, the equation of the line passing through the origin is y = 1x, which can be simplified as y = x.