Use the two table points $(1,155)$ and $(3,285)$. Ask: by how much does the charge increase when the hours go from $1$ to $3$? Then divide that change in charge by the change in hours.

Once you know the hourly rate $m$, plug it and one point from the table into $f(h) = mh + b$ to solve for $b$, the fee when $h=0$.

After you find an equation, substitute $h=1$ and $h=3$ to make sure it produces $155$ and $285$ respectively.

In Desmos, evaluate each option at $h=1$ by typing the expressions:

• $25*1+130$
• $130*1+25$
• $65*1+90$
• $90*1+65$ Compare each result to the table value $155$ to see which equations pass through $(1,155)$.

Now evaluate each option at $h=3$:

• $25*3+130$
• $130*3+25$
• $65*3+90$
• $90*3+65$ Look for the expression that equals $285$, because that equation matches the table value at $h=3$.

The only equation whose outputs match both $155$ when $h=1$ and $285$ when $h=3$ is the correct linear model; choose that one from the answer choices.

A linear relationship between hours $h$ and total charge $f(h)$ can be written as

where:

• $m$ is the hourly rate (slope), and
• $b$ is the starting fee when $h=0$ (the $y$-intercept).

Use the two points from the table: $(1,155)$ and $(3,285)$.

The slope $m$ is

So the plumber charges $65$ dollars per hour.

Substitute $m = 65$ and one point, for example $(1,155)$, into $f(h) = mh + b$:

So

The starting fee is $90$ dollars.

Now substitute $m = 65$ and $b = 90$ back into the linear form:

This equation matches both table values, so $f(h)=65h+90$ is the correct choice.