Question

The values in the table below represent Function B, which is a linear function.

Answer 1

1. Compare Functions B and L by determining which one has the greater rate of change.

The rate of change is expressed as the ratio between a change in one variable relative to a corresponding change in another. On the other hand, a linear function is given as the form:

$y=mx+b$

And $m$ is the rate of change we are looking for. For Function B we have a Table and the slope can be found by choosing two points, therefore:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ Choosing \ (1,5) \ and \ (3,11) \\ \\ m=\frac{11-5}{3-1}=3$

As you can see $y=6x+4$ has a rate of change of 6 while the function of the table has a rate of change of 3.

In conclusion, $y=6x+4$ has the greater rate of change

2. which one has a greater y-intercept?

We need to get the equation that rules the points given on the table. Two-Point Form of the Equation of a Line is:

$y-y_{1}=m(x-x_{1}) \\ \\ We \ know \ m=3 \\ \\ y-5=3(x-1) \therefore y-5=3x-3 \therefore y=3x+2$

As you can see $y=6x+4$ has a y-intercept of $b=4$ while the function of the table has a y-intercept of $b=2$

In conclusion, $y=6x+4$ also has the greater y-intercept