Question

. The slope of the function, g(x) is 5. What is the value of k if g(k) = 3 and g(5) = 2k?

Answer 1

Given that it is a linear function, we know the form:

$g(x)=mx+b$

m is slope.

Given slope is 5, we can write:

$g(x)=5x+b$

Now,

Given g(k) = 3, we can write:

$\begin{gathered} g(x)=5x+b \\ 3=5k+b \end{gathered}$

Again, given

g(5) = 2k, so we can write:

$\begin{gathered} g(x)=5x+b \\ 2k=5(5)+b \\ 2k=25+b \end{gathered}$

We have two equations is k and b. We can write both in terms of k and solve. Shown below:

Equation 1:

$\begin{gathered} 3=5k+b \\ b=3-5k \end{gathered}$

Equation 2:

$b=2k-25$

Now, we equate both of these equations and solve for k. Shown below:

$\begin{gathered} 3-5k=2k-25 \\ 3+25=2k+5k \\ 28=7k \\ k=\frac{28}{7} \\ k=4 \end{gathered}$

So, the value of k is 4.

k = 4 (answer)