Bob is analyzing two linear functions, f(x) and g(x). will they intersect? f(x) graph of the function f of x equals 2x + 3 g(x) x g(x) −2 4 −1 1 0 −2

The first function is given by equation

The second function is given by the table

To write the rule of g(x) you have to substitute two points into the equation

1) When x=-2, g(x)=4 and 4=-2a+b;

2)When x=-1, g(x)=1 and 1=-a+b.

Subtract from the second equation the first equation:

1-4=-a+b-(-2a+b),

-3=-a+b+2a-b,

-3=a.

If a=-3, then b=1+a=1-3=-2 and the equation of g(x) is g(x)=-3x-2.

The slopes of f(x) and g(x) are 2 and -3 respectively.

Since these numbers are different, the lines will not be parallel, thus, they will intersect.