A constant change in $y$ for each 1-unit change in $x$ is the slope $m$ in the equation $y = mx + b$. Use the pattern you found in the table to determine $m$.

Once you know $m$, pick any one point from the table, plug its $x$ and $y$ into $y = mx + b$, and solve for $b$. Then compare the resulting form of the equation to the answer choices.

Use the table feature and enter the four points from the problem: $(1,5)$, $(2,7)$, $(3,9)$, and $(4,11)$. You should see these four points plotted on the graph.

In separate expression lines, type each option exactly as given: $y = 3x - 2$, $y = 4x - 1$, $y = 5x$, and $y = 2x + 3$. Desmos will draw four different lines on the same coordinate plane.

Compare the lines with the plotted points. The correct equation is the one whose line goes exactly through all four points from the table; each incorrect equation will miss at least one of the points.

Look at how the values change:

• As $x$ goes from 1 to 2 to 3 to 4, it increases by 1 each time.
• As $y$ goes from 5 to 7 to 9 to 11, it increases by 2 each time.

A constant change in $y$ for each 1-unit change in $x$ suggests a linear relationship of the form $y=mx+b$ (a straight line).

The slope $m$ of a line is the change in $y$ divided by the change in $x$:

Using any two points from the table, for example $(1,5)$ and $(2,7)$:

So the slope of the line is $m = 2$. Any correct equation must have slope 2.

A line in slope-intercept form is written as $y = mx + b$.

You already know $m = 2$, so the equation has the form

Now use one point from the table, for example $(1,5)$, and substitute $x=1$ and $y=5$:

So the y-intercept is $b = 3$.

From the previous steps, the line must have slope 2 and y-intercept 3, so its equation is

Check quickly with one value from the table: if $x=1$, then $y = 2(1) + 3 = 5$, which matches the table. This corresponds to choice D, so the correct answer is $y = 2x + 3$.