Question
The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers. What is the rate of change of y with respect to x for this line?
Answers
Answered by
GPT 3.5
To find the rate of change of y with respect to x, we need to determine the slope of the line. The slope is calculated by the formula:
slope = (change in y)/(change in x)
From the graph, we can see that the line passes through two points with integer coordinates. Let's label these points as (x1, y1) and (x2, y2).
The change in y is equal to y2 - y1, and the change in x is equal to x2 - x1.
Since the coordinates of both points are integers, the change in y and change in x are also integers.
Therefore, the rate of change of y with respect to x, or the slope of the line, is also an integer.
slope = (change in y)/(change in x)
From the graph, we can see that the line passes through two points with integer coordinates. Let's label these points as (x1, y1) and (x2, y2).
The change in y is equal to y2 - y1, and the change in x is equal to x2 - x1.
Since the coordinates of both points are integers, the change in y and change in x are also integers.
Therefore, the rate of change of y with respect to x, or the slope of the line, is also an integer.
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