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Q: How can you use the unit rate or constant of proportionality for a relationship represent in a graph?

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A straight line, through the origin, sloping up from left to right. The gradient of the graph will be the constant of proportionality.

The slope of the speed/time graph is the magnitude of acceleration. (It's very difficult to draw a graph of velocity, unless the direction is constant.)

A coordinate graph is a graph of pairs of numbers that represent real-life situations.

Motion at a constant speed - no acceleration or deceleration.

Constant variation is a relationship between two variables where one is a fixed multiple of the other. The graph of such a relationship is a straight line through the origin.

Related questions

The answer depends on what the constant is: the y-intercept in a linear graph, constant of proportionality, constant of integration, physical [universal] constant.

Direct proportionality. Their graph would be a straight line through the origin, with the slope equal to the ratio.

The graph of a relationship in which two variables are in direct proportion is a straight line through the origin, whose slope = the rate of change = the constant of proportionality.

In a table, divide a number in one column by the corresponding number in the other column. In a graph it is the gradient of the line. The equation, for the variables X and Y will be of the form Y = mX and the constant of proportionality is m.

A scatter plot will show the data points on a straight line through the origin, whose slope is the constant of proportionality.

A straight line, through the origin, sloping up from left to right. The gradient of the graph will be the constant of proportionality.

dependent

constant speed

y = cx where c is some non-zero constant of proportionality. Equivalently, x = ky where k (= 1/c) is a constant of proportionality. The graph of y against x is a straight line through the origin, with slope c.

The slope of the speed/time graph is the magnitude of acceleration. (It's very difficult to draw a graph of velocity, unless the direction is constant.)

That the object is moving at a constant speed

A coordinate graph is a graph of pairs of numbers that represent real-life situations.