Question 183·Easy·Algebra

Once you know the slope, put it into the slope-intercept form $y = mx + b$ and use one of the points to find $b$.

After you get an equation, plug in both given points to make sure they satisfy the equation (both $x$ and $y$ should work).

In Desmos, click the "+" icon, choose "Table," and enter $x$-values $2$ and $6$ with corresponding $y$-values $-3$ and $5$ to plot the points $(2,-3)$ and $(6,5)$.

In separate lines, type each option exactly as written: y = 2x + 7, y = 1/2 x - 7, y = -2x - 7, and y = 2x - 7. Desmos will graph four lines.

Look at the graph and identify which of the four lines goes exactly through both plotted points $(2,-3)$ and $(6,5)$. The corresponding equation is the correct answer.

Use the slope formula for a line through $(x_1,y_1)$ and $(x_2,y_2)$:

Here $(x_1,y_1) = (2,-3)$ and $(x_2,y_2) = (6,5)$, so

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

The slope-intercept form of a line is

where $m$ is the slope and $b$ is the $y$-intercept.

Substitute $m = 2$ into this form:

Use either of the given points to find $b$. Let's use $(2,-3)$.

Substitute $x = 2$ and $y = -3$ into $y = 2x + b$:

Simplify:

Subtract $4$ from both sides:

So the $y$-intercept is $b = -7$.

Now substitute $b = -7$ back into $y = 2x + b$:

Compare with the answer choices; this matches choice D) $y = 2x - 7$.