Pick any two pairs, for example $(1,4)$ and $(3,9)$. Use $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ to find the slope.

Once you know the slope $m$, write $y = mx + b$ and plug in the coordinates of any one point from the table to solve for $b$.

After you find both the slope and the $y$-intercept, compare them to the equations in the answer choices to see which one has the same $m$ and $b$.

Create a table and enter the $x$-values (1, 3, 5, 7, 9) in the first column and the corresponding $y$-values (4, 9, 14, 19, 24) in the second column. You should see five points plotted.

In separate lines, type each of the four equations exactly as given in the choices (for example, y = 2x + 2, y = 1.5x + 2.5, etc.). Four straight lines will appear on the graph.

Look at how each line lines up with the five plotted points from the table. The correct equation is the one whose line passes exactly through all five points; the others will miss at least some of the points.

Look at how $x$ and $y$ change together across the table:

• $x$: $1, 3, 5, 7, 9$ (increases by $2$ each time)
• $y$: $4, 9, 14, 19, 24$ (increases by $5$ each time)

Because the change in $y$ is constant for equal changes in $x$, the relationship is linear, so it can be written as $y = mx + b$ for some slope $m$ and intercept $b$.

For a linear relationship, the slope $m$ is

From the table:

• When $x$ goes from $1$ to $3$, $x$ increases by $2$.
• When $y$ goes from $4$ to $9$, $y$ increases by $5$.

So the slope is

You can keep it as a fraction or convert it to a decimal.

Start with the slope-intercept form $y = mx + b$ and plug in the slope you found and any point from the table.

Using the point $(1,4)$ and $m = \frac{5}{2}$:

Now solve this equation for $b$ (the $y$-intercept).

From the previous step:

Subtract $\frac{5}{2}$ from both sides:

Convert $4$ to halves: $4 = \frac{8}{2}$, so

which means $b = \frac{3}{2} = 1.5$.

So the equation is

which matches choice D.