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:
[tex]y=mx+b[/tex]
And [tex]m[/tex] 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:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ Choosing \ (1,5) \ and \ (3,11) \\ \\ m=\frac{11-5}{3-1}=3[/tex]
As you can see [tex]y=6x+4[/tex] has a rate of change of 6 while the function of the table has a rate of change of 3.
In conclusion, [tex]y=6x+4[/tex] 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:
[tex]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[/tex]
As you can see [tex]y=6x+4[/tex] has a y-intercept of [tex]b=4[/tex] while the function of the table has a y-intercept of [tex]b=2[/tex]
In conclusion, [tex]y=6x+4[/tex] also has the greater y-intercept
