Use the two given points to compute the slope (rate of change) of the line: $m = \dfrac{\text{change in } B}{\text{change in } d}$. This tells you how many dollars per gigabyte the plan charges.

Once you know the slope, write $B$ as a linear function of $d$ in the form $B = md + b$. Use one of the points to solve for $b$, then plug in $B = 67$ and solve for $d$.

Is your value of $d$ between 5 GB and 15 GB, as the problem states? If not, recheck your algebra and arithmetic.

In Desmos, type (6,45) and (14,85) on separate lines to plot the two known points. Then type y1 ~ m x1 + b on a new line; Desmos will fit a line through the points and show values for m and b. Note the exact values of m (slope) and b (intercept).

On a new line, enter the function using those m and b values, for example y = m x + b. On another line, enter y = 67 to represent the $67 bill as a horizontal line.

Tap the point where the line y = m x + b intersects the horizontal line y = 67. The x‑coordinate of this intersection is the number of gigabytes the customer used according to the model.

The bill $B$ is a linear function of data $d$.

We can treat each customer as a point $(d,B)$ on a line:

• The first customer: 6 GB and $45 $\Rightarrow$ point $(6,45)$.
• The second customer: 14 GB and $85 $\Rightarrow$ point $(14,85)$.

We want to find $d$ when $B = 67$ (a point $(d,67)$ on the same line).

For a linear function, the slope $m$ is the rate of change:

Compute this:

So the plan charges $5 for each additional gigabyte of data in this range.

Use slope–intercept form $B = md + b$, where $m$ is the slope and $b$ is the fixed base fee.

We already know $m = 5$, so start with

Plug in one of the known points, for example $(6,45)$, to find $b$:

So the equation relating bill and data is

Now set $B = 67$ and solve for $d$:

Subtract 15 from both sides:

Divide both sides by 5:

So a customer who paid $67 used 10.4 gigabytes, which corresponds to answer choice B.