You now have two equations with $p$ and $q$. How can you combine them (by subtracting one from the other) to make $q$ disappear so you can solve for $p$ first?

Once you find $p$, plug it back into one of your original equations (like the one from $(2,5)$) and solve that equation for $q$.

After you find $q$, substitute both $p$ and $q$ into $g(x)=px+q$ and check with one of the other given points to confirm your values are correct.

In Desmos, type (17-5)/(6-2) to compute the slope between the points $(2,5)$ and $(6,17)$. The result is the value of $p$ in $g(x)=px+q$.

Now type 5 - 2*(result) or, more explicitly, 5 - 2*((17-5)/(6-2)). This expression comes from rearranging $5 = 2p + q$ to $q = 5 - 2p$, and the value that Desmos outputs is the value of $q$ you need to choose from the options.

Because each point $(x,y)$ lies on the line $g(x)=px+q$, it must satisfy $y=px+q$.

Use two of the points, for example $(2,5)$ and $(6,17)$:

• From $(2,5)$: $5 = 2p + q$
• From $(6,17)$: $17 = 6p + q$

Now you have a system of two equations with the two unknowns $p$ and $q$.

Subtract the first equation from the second to eliminate $q$:

$17 = 6p + q$

$5 = 2p + q$

Subtracting gives:

• Left side: $17 - 5$
• Right side: $(6p + q) - (2p + q)$

So you get $12 = 4p$, which leads to a specific value for $p$.

From $12 = 4p$, divide both sides by $4$ to find $p$.

Then substitute that value of $p$ into one of the original equations, such as $5 = 2p + q$, to form an equation that has only $q$ in it. Solve this simple linear equation for $q$, but do not worry yet about the final numerical value; that will be your last step.

From $12=4p$, $p=3$. Substitute into $5=2p+q$ to get $5=2(3)+q$, so $5=6+q$, which simplifies to $q=-1$.

Therefore, the value of $q$ is $-1$.