Respuesta :

Answer:

-7

Step-by-step explanation:

If the function is linear, then it doesn't matter what two points are chosen to find the slope because the slope is constant.

So that is the following should be true in this case:

[tex]\frac{g(2)-g(-2)}{2-(-2)}=\frac{g(-5)-g(2)}{-5-2}[/tex]

Let's solve this!

Firstly, I'm going to replace [tex]g(2)[/tex] with 7 and [tex]g(-2)[/tex] with -1:[tex]\frac{7-(-1)}{2-(-2)}=\frac{g(-5)-7}{-5-2}[/tex]

Now, I'm going to perform any arithmetic I can:

[tex]\frac{8}{4}=\frac{g(-5)-7}{-7}[/tex]

[tex]2=\frac{g(-5)-7}{-7}[/tex]

Now I want to get the thing that contains the variable by itself.

The variable I'm referring to is [tex]g(-5)[/tex].

So we need to get [tex]g(-5)-7[/tex] by itself first.

It is being divided by -7.

So we will multiply both sides by -7 giving us:

[tex]2(-7)=g(-5)-7[/tex]

[tex]-14=g(-5)-7[/tex]

We are now going to add 7 on both sides:

[tex]-14+7=g(-5)[/tex]

[tex]-7=g(-5)[/tex]

So [tex]g(-5)[/tex] has value -7.

So this means we know the following points are on this line:

[tex](2,7),(-2,-1),\text{ and }(-5,-7)[/tex].

Let's confirm that we get the same slope no matter the two points we use:

Test 1: [tex](2,7) \text{ and } (-2,-1)[/tex]

Line them up and subtract and then put 2nd difference over first:

[tex](2,7)[/tex]

-[tex](-2,-1)[/tex]

---------------------

     4    , 8

So the slope is 8/4=2.

Test 2: [tex](2,7) \text{ and } (-5,-7)[/tex]

Line them up and subtract and then put 2nd difference over first:

[tex](2,7)[/tex]

-[tex](-5,-7)[/tex]

---------------------

     7    , 14

So the slope is 14/7=2.

Test 3: [tex](-5,-7) \text{ and } (-2,-1)[/tex]

Line them up and subtract and then put 2nd difference over first:

[tex](-5,-7)[/tex]

-[tex](-2,-1)[/tex]

---------------------

     -3 ,  -6

So the slope is -6/-3=2.

So all 3 tests work.

There was only 3 tests since 3 choose 2=3.