Question

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.

Answer 1

`k=-66`

Explanation:

So we are given two values:

`g(4)=9 \text{ and } g(-11)=k`

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:

`m=(y_2-y_1)/(x_2-x_1)`

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

`5=(k-9)/(-11-4)`

Simplify the denominator:

`5=(k-9)/(-15)`

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

`-15(5)=(-15)(k-9)/(-15)\\ -75=k-9`

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

`(-75)+9=(k-9)+9\\k=-66`

Therefore, k is -66.