Given that g(4)=9 and g(-11)=k, find the value of k that would result in a slope of 5 between the two points.

Step-by-step explanation:

So we are given two values:

They can be interpreted as: (4,9) and (-11,k).

So, we want to find the value of k such that the slope of the line between the two points would be 5.

Recall the slope formula. It is:

Let (4,9) be x₁ and y₁ and let (-11,k) be x₂ and y₂. Substitute 5 for m. Therefore:

Simplify the denominator:

Multiply both sides by -15. The right side cancels:

Now, add 9 to both sides. The right side cancels.

Therefore, k is -66.