Question Video: Comparing the 𝑦-Intercept of Two Linear Functions given the Graph of One of Them and the Function Table of the Other Mathematics • 8th Grade

Which of the following functions has a greater 𝑦-intercept?

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Video Transcript

Which of the following functions has a greater 𝑦-intercept?

For function a, we can look on the graph. The 𝑦-intercept is the place that crosses the 𝑦-axis. And this function crosses the 𝑦-axis at two.

For function b, it’s not as immediately apparent what the 𝑦-intercept is.

There are a few options. First, we recognize that the 𝑦-intercept is always found at the point 𝑥 is zero. When 𝑥 equals zero, we have our 𝑦-intercept. We can also notice the rate of change for this function.

As 𝑥 moves up one, we add four to the 𝑦-values. The rate of change is then four over one. We also call this the slope.

And that means that to go from negative one to zero is an increase of one on the 𝑥-axis and would need an increase of four on the 𝑦-axis. Negative three plus four equals one.

Function b has an intercept at the point zero, one. If we wanted to confirm this, we could plot the other points on the graph.

Taking a second look at the graph confirms that function a has the greater 𝑦-intercept.

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