Compare $5p - 3$ with $15p - 9$. What number multiplies $5$ to get $15$ and multiplies $-3$ to get $-9$?

Once you know the multiplier from the previous hint, rewrite $15p - 9$ as that number times $(5p - 3)$. Then use the fact that $5p - 3 = 27$ to replace it with a number you already know.

In Desmos, use $x$ in place of $p$. Enter y = 5x - 3 and y = 27. Find the intersection point of the two graphs and note the $x$-coordinate; this is the value of $p$ that makes $5p - 3 = 27$ true.

In the Desmos input bar, type 15*(value) - 9, replacing value with the $x$-coordinate you found in Step 1. The resulting number shown by Desmos is the value of $15p - 9$ and corresponds to the correct answer choice.

Look at the given expression $5p - 3$ and the expression you are asked about, $15p - 9$.

• The coefficient of $p$ changed from $5$ to $15$.
• The constant changed from $-3$ to $-9$.

Both parts were multiplied by $3$, so you can rewrite

You are told that $5p - 3 = 27$. Substitute this value into the expression from Step 1:

Now the problem is just to evaluate $3 \times 27$. Do this carefully.

Compute the product:

So $15p - 9 = 81$, which corresponds to answer choice D.