The constant amount that $y$ changes when $x$ increases by 1 is the slope $m$ in the equation $y=mx+b$. Find that value from the table.

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

After you get an equation, substitute $x=1,2,3$ and make sure it gives $y=11,16,21$. Only one choice will work for all three points.

Create a table in Desmos with $x$-values 1, 2, 3 in the first column and $y$-values 11, 16, 21 in the second column. You should see three plotted points.

On separate lines, type each option exactly as given (for example, y = 5x + 11, y = 6x + 5, etc.). Desmos will draw a line for each equation.

Look at which line passes through all three plotted points from the table. The equation whose graph goes exactly through all points is the correct choice.

Look at how $y$ changes as $x$ increases:

• When $x$ goes from 1 to 2, $y$ goes from 11 to 16, an increase of $5$.
• When $x$ goes from 2 to 3, $y$ goes from 16 to 21, again an increase of $5$.

So, for each increase of 1 in $x$, $y$ increases by 5. This means the slope (rate of change) is $m=5$.

A linear relationship can be written in slope-intercept form:

You already found $m=5$, so the equation must look like

for some constant $b$ (the $y$-intercept).

Pick any $(x,y)$ pair from the table, for example $(1,11)$, and substitute into $y = 5x + b$:

Simplify:

Subtract 5 from both sides:

Now substitute $b=6$ back into $y = 5x + b$:

Compare with the answer choices: this matches choice D, so the correct equation is $y = 5x + 6$.