Use the first and last points to compute an approximate slope $\frac{\Delta y}{\Delta x}$. Then, look at the slopes in the four equations (the numbers multiplying $x$). Which are obviously too small or too large?

Once you know a good estimate for the slope, plug that slope and any one $(x, y)$ pair from the table into $y = mx + b$ to solve for $b$. Then match this approximate intercept to the choices.

In Desmos, create a table and enter the $x$-values (4.7, 5.0, 5.5, 6.1, 6.5, 6.8) in the first column and the corresponding $y$-values (135, 145, 155, 170, 182, 190) in the second column. You should see six plotted points.

On new lines in Desmos, type each option exactly: y = 15x + 26, y = 26x + 15, y = 40x - 60, and y = 60x - 40. All four lines will appear on the same coordinate plane along with the data points.

Look at how close each line is to the six data points overall. Focus on which line stays nearest to most of the points (not just one point). The equation whose line best follows the cluster of points is the model you should choose.

The question says the data follow a roughly linear trend, so we want an equation of the form $y = mx + b$, where:

• $m$ is the slope (change in mass for each 1-inch change in screen size), and
• $b$ is the $y$-intercept.

We will estimate $m$ from the table and then find $b$.

Use the first and last data points to estimate the slope:

• First point: $(4.7, 135)$
• Last point: $(6.8, 190)$

Compute the changes:

• Change in $x$: $6.8 - 4.7 = 2.1$
• Change in $y$: $190 - 135 = 55$

So the slope is approximately

Look at the answer choices: their slopes are 15, 26, 40, and 60. Only one choice has a slope close to 26, so all lines with slopes far from 26 can be eliminated.

Now use the approximate slope $m \approx 26$ with any data point to estimate $b$.

Using the point $(4.7, 135)$ in $y = mx + b$:

Compute $26 \cdot 4.7$:

So

The intercept should be around 13. Compare this to the intercepts in the answer choices: 26, 15, $-60$, and $-40$. The only one near 13 is the line with intercept 15.

Take the equation with slope 26 and intercept 15 and test it on another data point, say $x = 6.5$ (which has actual $y = 182$):

Compute:

The predicted mass $184$ g is very close to the actual $182$ g, and similar checks work for other points. Therefore, the equation that best models the relationship is $y = 26x + 15$.