Question 77·Medium·Linear Functions

Slope is the change in $y$ over the change in $x$. If the slope is $-4$, what does that tell you about how $y$ changes when $x$ increases by $1$?

How much does $x$ change when you go from $-2$ to $5$? Multiply that change by the slope to find how much $y$ changes, then apply that to the starting value $7$.

In Desmos, enter the expression 7 + (-4)*(5 - (-2)). This uses the starting value $7$ at $x=-2$, the slope $-4$, and the change in $x$ from $-2$ to $5$. The numeric result shown is the value of $p(5)$.

The statement $p(-2)=7$ means that the point $(-2, 7)$ lies on the line representing the function $p$.

We also know the slope of this line is $-4$. Slope is the change in y divided by the change in x.

We want to find $p(5)$, which corresponds to the point $(5, p(5))$.

Compute the change in $x$ from $-2$ to $5$:

So $x$ increases by $7$ units.

A slope of $-4$ means that for every increase of $1$ in $x$, $y$ decreases by $4$.

If $x$ increases by $7$, then the change in $y$ is:

We start at $y = 7$ when $x = -2$, so at $x = 5$:

So the value of $p(5)$ is $-21$.