The first function is given by equation [tex]f(x)=2x+3.[/tex]
The second function is given by the table
[tex]\begin{array}{cccc}x&-2&-1&0\\f(x)&4&1&-2\end{array}[/tex]
To write the rule of g(x) you have to substitute two points into the equation
[tex]g(x)=ax+b.[/tex]
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.
