Question

Use the description to answer the question.

An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line line passes through points plotted at left parenthesis 3 comma 3 right parenthesis and left parenthesis 8 comma 8 right parenthesis.
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
Responses

y = 3x

y = 3/3 x

y = x

y = 8x

Answer 1

[AI-generated answer — Bot GPT 3.5]

Using the graph, we can see that the line passes through the origin, which is the point (0,0). The line also passes through the point (3,3), which means that the rise and run of the line is 3 units. Therefore, the slope (m) of the line is 3/3 or 1.

The equation of the line can be written as y = mx, where m is the slope. Substituting in the value of m, we get y = 1x.

Simplifying the numerical coefficient, we get y = x.

So, the correct equation for a line through the origin on the given graph is y = x.