Question

Use the image to answer the question. The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin. (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To derive the equation of the line y=mx through the origin, we need to find the value of the slope (m).

Looking at the graph, we can see that the line passes through the origin, which means the y-intercept is zero (b = 0). Therefore, the equation of the line can be simplified to y = mx.

To find the slope, we can use the formula: m = (change in y) / (change in x).

Looking at the graph, we can see that as x increases by 2 units, y increases by 4 units. Therefore, the change in y is 4 and the change in x is 2.

Plugging these values into the slope formula, we get:
m = 4 / 2
m = 2

Therefore, the equation of the line y=mx through the origin is y = 2x.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To derive the equation of the line y = mx through the origin, we need to find the slope, m. The slope of a line is given by the change in y divided by the change in x.

Looking at the graph, we can see that for every unit increase in x, there is a corresponding unit increase in y. Therefore, the change in y is the same as the change in x, leading to a slope of 1.

Since the line passes through the origin (0,0), the equation of the line y = mx becomes y = 1x or simply y = x.

Answer 3

[AI-generated answer — Explain Bot]

To derive the equation of the line y = mx through the origin using the given graph, you can follow these steps:

1. First, identify two points on the graph that lie on the line. These points should pass through the origin (0,0) since we want to find the equation through the origin.

2. Once you have identified two points, determine the slope (m) of the line using the formula: m = (change in y) / (change in x).

3. To find the change in y, subtract the y-coordinates of the two points. Similarly, subtract the x-coordinates to find the change in x. Note that since the line passes through the origin, one of the points will have coordinates (0, 0).

4. Divide the change in y by the change in x to find the slope (m).

5. Now that you have the slope (m), you can use it to write the equation of the line in the form y = mx, where m is the slope.

It's important to note that without an actual image or specific data points, I can only provide general guidance on how to derive the equation of the line through the origin. You will need to refer to the given graph or provide specific data points to obtain a more accurate result.