The problem says the temperature rises 3°F every 2 hours. How many degrees does it rise in 1 hour? Write this as a fraction.

In an equation of the form $T = mh + b$, which part shows how fast the temperature changes per hour, and which part shows the starting temperature?

In Desmos, use $x$ in place of $h$. Enter each option on its own line:

• y = 58 + (2/3)x
• y = 58 + 3x
• y = 58 + (3/2)x
• y = 58 + x/3

For each equation, either look at the graph where $x=0$ or create a table (click the gear icon and select "Table"). Confirm that when $x=0$, $y$ is 58 for all four lines, matching the temperature at 6 a.m.

In the table for each line, enter $x=2$ (2 hours after 6 a.m.). The real situation says the temperature should be exactly 3°F higher than 58°F at this time. Identify which line’s table shows this correct increase from $x=0$ to $x=2$; that line represents the correct model.

At 6 a.m., which corresponds to $h=0$, the temperature was 58°F.

So when $h=0$, we should have $T=58$. This tells us the equation must have a $+58$ as the constant term (the $y$-intercept).

The temperature rises 3°F every 2 hours.

To write a linear equation in the form $T = mh + b$, the coefficient $m$ must be the change in temperature per 1 hour.

Compute the rate per hour:

So the slope (rate) in our equation is $\tfrac{3}{2}$. This will be the coefficient of $h$.

A linear model with starting value 58°F and rate $\tfrac{3}{2}$ degree per hour has the form

So the correct equation is $T = 58 + \tfrac{3}{2}h$. This matches answer choice C.