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
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.