Question 91·Easy·Linear Equations in Two Variables

Once you know the slope $m$, write the equation in the form $y = mx + b$ and plug in the coordinates of one of the given points to find $b$.

After you find an equation, plug both $(4,-2)$ and $(8,6)$ into it to make sure they both satisfy the equation before choosing your answer.

Enter the points $(4,-2)$ and $(8,6)$ into Desmos, either by typing them directly or by creating a table and adding the two points. Make sure both points appear on the graph.

In separate lines, type each option: y = 2x + 10, y = -2x - 10, y = -2x + 10, and y = 2x - 10. You will see four different lines on the same coordinate plane.

Look at each line and check which one goes exactly through both plotted points, $(4,-2)$ and $(8,6)$. The equation of that line is the correct answer choice.

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

Here, use $(4,-2)$ as $(x_1,y_1)$ and $(8,6)$ as $(x_2,y_2)$:

So, the slope of line $\ell$ is $m=2$. Keep this value for the next step.

Write the slope-intercept form of a line: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

You already know $m=2$, so the equation becomes $y = 2x + b$.

Now plug in the coordinates of one of the given points (for example, $(4,-2)$) to solve for $b$:

• Substitute $x=4$ and $y=-2$ into $y = 2x + b$.

Solve for $b$ by subtracting $8$ from both sides:

So the y-intercept is $b=-10$.

Substitute the slope $m=2$ and the y-intercept $b=-10$ into $y = mx + b$:

Compare this with the answer choices; it matches choice D, so the correct equation is $y = 2x - 10$.