Use the two points to calculate the slope $m$ with the formula $m = \frac{y_2-y_1}{x_2-x_1}$. Is the slope positive or negative?

Once you know the slope, look at the coefficient of $x$ in each option to see which ones are even possible.

After narrowing down the choices, substitute $x=-3$ or $x=1$ into the remaining equations to see which one gives the correct function value.

In Desmos, type each option as its own line:

• y = 2x + 4
• y = -2x + 4
• y = -2x - 4
• y = 2x - 4

Add the points (-3, 10) and (1, 2) in Desmos (just type them exactly like that on new lines). They will appear as points on the graph.

Look at which of the four lines passes exactly through both plotted points. The line that goes through both $(-3,10)$ and $(1,2)$ corresponds to the correct equation.

A linear function $p$ can be written as a line on the coordinate plane.

The statements:

• $p(-3)=10$
• $p(1)=2$

mean that the graph of $p$ passes through the two points $(-3,10)$ and $(1,2)$.

Use the slope formula with the points $(-3,10)$ and $(1,2)$:

So the slope of the line (and of the function $p$) is $m=-2$.

In a linear equation written as $y=mx+b$, the coefficient of $x$ is the slope $m$.

Look at each option's coefficient of $x$:

• A) $p(x)=2x+4$ has slope $2$.
• B) $p(x)=-2x+4$ has slope $-2$.
• C) $p(x)=-2x-4$ has slope $-2$.
• D) $p(x)=2x-4$ has slope $2$.

Since we found the slope must be $-2$, only choices B and C are still possible.

Now plug $x=-3$ into each of the remaining choices (B and C) and see which one gives $p(-3)=10$:

• Choice B: $p(x)=-2x+4$
  • $p(-3)=-2(-3)+4=6+4=10$, which matches the given value.
• Choice C: $p(x)=-2x-4$
  • $p(-3)=-2(-3)-4=6-4=2$, which does not match $10$.

Therefore, the function that fits both given conditions is $p(x)=-2x+4$.