Use the two points to find the slope: what is the change in temperature divided by the change in time?

Once you know the slope, write $F(t) = mt + b$ and plug in one of your points to solve for $b$.

Make sure your equation gives 180°F at $t = 5$ and 140°F at $t = 9$, and that the temperature decreases (not increases) as time increases.

In Desmos, type (5, 180) and on the next line (9, 140) so you can see the two points the line must pass through.

Treat $t$ as $x$ in Desmos. Enter each option as a separate line: y = 230 - 40x, y = 230 - 10x, y = 180 - 10x, and y = 140 + 10x. Observe which line passes exactly through both plotted points.

Look at the line that goes through both points and note how quickly it goes down as $x$ increases by 1. The vertical drop per 1 unit of $x$ should match the temperature change per minute described in the problem.

The function $F(t)$ gives temperature (in °F) based on time (in minutes).

• After 5 minutes, the temperature is 180°F, so that is the point $(5, 180)$.
• After 9 minutes, the temperature is 140°F, so that is the point $(9, 140)$.

So the line must pass through $(5, 180)$ and $(9, 140)$.

Use the slope formula (change in $y$ over change in $x$):

So the slope of the line is $-10$. This means the temperature decreases by 10°F each minute.

Use the slope-intercept form $y = mx + b$, but here the variables are $t$ and $F(t)$, so we write $F(t) = mt + b$.

We already know $m = -10$. Substitute $m = -10$ and one point, say $(5, 180)$:

Compute $-10(5)$:

Add 50 to both sides:

So the y-intercept is $230$.

Now plug the slope $m = -10$ and intercept $b = 230$ into $F(t) = mt + b$:

We can rewrite this as

which matches answer choice B.