Once you know the slope $m$, write the equation of the line in the form $y = mx + b$, leaving $b$ unknown for now.

Pick either $(2,3)$ or $(4,7)$ and substitute the $x$- and $y$-values into your equation $y = mx + b$ to solve for $b$.

After you find $m$ and $b$, compare your equation with the options and also verify that your equation gives the correct $y$-values for both $x = 2$ and $x = 4$.

In Desmos, click the "+" and choose "Table." Enter $2$ and $4$ in the $x$-column and $3$ and $7$ in the $y$-column so the points $(2,3)$ and $(4,7)$ appear on the graph.

On separate lines, type each option exactly as an equation (for example, y = 2x + 1, then on another line y = -2x + 1, etc.) so four different lines appear on the graph.

Look at which of the four lines passes through both plotted points $(2,3)$ and $(4,7)$. The option whose line goes exactly through both points is the correct equation.

You are given two points on the line: $(2,3)$ and $(4,7)$. To find the slope, first compute how much $x$ and $y$ change when you go from the first point to the second:

• Change in $x$: $4 - 2 = 2$
• Change in $y$: $7 - 3 = 4$.

The slope $m$ of a line through two points is

Substitute the changes you found:

So the slope of the line is $m = 2$.

A line with slope $m$ can be written as $y = mx + b$, where $b$ is the $y$-intercept.

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

Now you need to find the value of $b$ using one of the points on the line.

Use point $(2,3)$, which lies on the line. Substitute $x = 2$ and $y = 3$ into $y = 2x + b$:

So

Therefore, the equation of the line is $y = 2x - 1$, which corresponds to choice D.