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Question Video: Writing the Function Represented by a Graph Mathematics • 7th Grade

Write the function that is represented by the graph.

01:26

Video Transcript

Write the function that is represented by the graph.

If we think about the 𝑦-intercept form, 𝑦 equals π‘šπ‘₯ plus 𝑏, we need the slope of the line and the 𝑦-intercept to write its function. The 𝑦-intercept is the place where the line crosses the 𝑦-axis.

Notice here that the 𝑦-axis is being called 𝑓 of π‘₯, the function of π‘₯. We can also say 𝑓 of π‘₯ equals π‘šπ‘₯ plus 𝑏.

But back to the 𝑦-intercept. The place where it crosses the 𝑦-axis on this graph is three. 𝑓 of π‘₯ equals the slope times π‘₯ plus three.

To find the slope, let’s consider the changes in 𝑦 over the changes in π‘₯.

Here’s an example. As we go down two from three, so down two on the 𝑦-axis, we go over three on the π‘₯-axis. Down two, right three gives us a slope of negative two-thirds. And we’ve already considered that the 𝑦-intercept is three.

The function represented by this graph is 𝑓 of π‘₯ equals negative two-thirds π‘₯ plus three.

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