# Question Video: Writing the Function Represented by a Graph Mathematics • 8th Grade

Write the function that is represented by the graph.

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### Video Transcript

Write the function that is represented by the graph.

If we think about the π¦-intercept form, π¦ equals ππ₯ plus π, we need the slope of the line and the π¦-intercept to write its function. The π¦-intercept is the place where the line crosses the π¦-axis.

Notice here that the π¦-axis is being called π of π₯, the function of π₯. We can also say π of π₯ equals ππ₯ plus π.

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

To find the slope, letβs consider the changes in π¦ over the changes in π₯.

Hereβs an example. As we go down two from three, so down two on the π¦-axis, we go over three on the π₯-axis. Down two, right three gives us a slope of negative two-thirds. And weβve already considered that the π¦-intercept is three.

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