Question 86·Medium·Linear Equations in Two Variables

Once you know the slope $m$, write the line as $y = mx + b$ and plug in one of the given points to solve for $b$, the $y$-intercept.

After you find an equation, plug in the other point to confirm it lies on the line. The correct equation must work for both given points.

In Desmos, type (-3, 2) and (5, -2) on separate lines to plot the two points that the correct line must pass through.

On new lines, enter each option exactly as written: y = 2x - 4, y = -1/2 x + 1/2, y = -1/2 x - 1/2, and y = 1/2 x + 1/2. Four lines will appear on the graph.

Look at which of the four lines passes through both plotted points $(-3,2)$ and $(5,-2)$. The equation of that line is the correct answer choice.

Use the slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$:

Let $(-3,2)$ be $(x_1,y_1)$ and $(5,-2)$ be $(x_2,y_2)$:

So the slope of line $\ell$ is $m = -\tfrac12$.

Slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

We already know $m = -\tfrac12$, so the equation must look like

Now we just need to find $b$.

Substitute one of the given points into $y = -\tfrac12 x + b$ to find $b$. Use $(-3,2)$:

• $x = -3$
• $y = 2$

So:

Compute $-\tfrac12(-3) = \tfrac32$, so:

Subtract $\tfrac32$ from both sides:

So the $y$-intercept is $b = \tfrac12$.

From the previous steps, the line has slope $-\tfrac12$ and $y$-intercept $\tfrac12$, so its equation is

Among the answer choices, this matches choice B.