Question 86·Medium·Linear Functions

Once you have the two points, use the slope formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ to find the slope of the line.

After finding the slope, write the equation in the form $y=mx+b$ using that slope, and then plug in one of the points to solve for $b$.

When you have an equation, compare its slope and intercept to each answer choice, or plug one of the given points into each choice to see which one works.

In Desmos, enter each option on its own line: y=-x-5, y=x+5, y=x-5, and y=-x+5. This will display the four possible lines.

Add the points (-4,9) and (11,-6) in Desmos (for example, type (-4,9) and (11,-6) on separate lines). These represent the conditions $g(-4)=9$ and $g(11)=-6$.

Look at the graph and see which of the four lines passes exactly through both plotted points. The equation of that line is the correct choice.

Because $g$ is linear and you are told $g(-4)=9$ and $g(11)=-6$, you can think of these as two points on the graph of $g$:

• Point 1: $(-4,9)$
• Point 2: $(11,-6)$

The question is asking for the equation of the line that passes through these two points.

Use the slope formula with the two points $(-4,9)$ and $(11,-6)$:

So the slope of the line is $m=-1$.

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

You found $m=-1$, so the equation has the form

for some value of $b$ that you still need to find.

Substitute one of the known points into $y=-x+b$ to find $b$. Use $(-4,9)$:

So the $y$-intercept is $b=5$.

You found that the equation of $g$ is

Among the choices, this corresponds to choice D.