In a linear equation of the form $p = mn + b$, the value of $p$ when $n = 0$ tells you $b$. Look at the table entry for $n = 0$.

Once you know the slope and the intercept $b$, plug them into $p = mn + b$ and then compare your result to the answer choices.

After you pick an equation, plug in $n = 0$, $1$, and $3$ to see if it gives $p = -4$, $2$, and $14$. The correct equation must work for all three.

In Desmos, type the three ordered pairs from the table as points: (0, -4), (1, 2), and (3, 14). You should see three points on the graph.

Enter each option as a separate line in Desmos: p = -4n + 6, p = 4n - 6, p = 6n - 4, and p = 6n + 4. Desmos will draw four lines.

Look at the graph and find which of the four lines passes exactly through all three points from the table. The equation of that line is the correct choice.

For a linear relationship, the slope is the change in $p$ divided by the change in $n$.

From $n=0$ to $n=1$:

• $p$ goes from $-4$ to $2$, so the change in $p$ is $2 - (-4) = 6$.
• The change in $n$ is $1 - 0 = 1$.

So the slope is $\dfrac{6}{1} = 6$.

In an equation like $p = mn + b$, the number $b$ is the value of $p$ when $n = 0$.

From the table, when $n = 0$, $p = -4$. So the y-intercept $b$ is $-4$.

A linear equation relating $p$ and $n$ can be written in the form $p = mn + b$, where $m$ is the slope and $b$ is the y-intercept.

From the earlier steps, you know:

• The slope $m$ is $6$.
• The y-intercept $b$ is $-4$.

Now substitute these values of $m$ and $b$ into $p = mn + b$.

Substituting $m = 6$ and $b = -4$ into $p = mn + b$ gives

This matches answer choice C, so the correct equation is $p = 6n - 4$.