You are told the slope is $-3$. Look at the coefficient of $x$ in each answer choice and eliminate any equation that does not have slope $-3$.

For the remaining choices, substitute $x=-1$ into the equation and see what $y$ value you get. Which equation gives $y=5$ when $x=-1$?

For any remaining options with slope $-3$, plug in $x=-1$ and see which gives $y=5$. The one that does is the correct equation.

Type each option into Desmos on its own line:

• y=-3x+8
• y=3x+2
• y=3x+8
• y=-3x+2 This will graph all four lines on the same coordinate plane.

In a new line, type the point as (-1,5). Desmos will show this as a dot on the graph.

Look at which of the graphed lines has slope $-3$ (the coefficient of $x$ is $-3$) and also passes exactly through the point (-1,5). The equation of that line, as shown in the expressions list, is the correct answer.

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

You are told the slope is $-3$, so substitute $m=-3$ to get

Now you just need to find $b$ using the given point $(-1,5)$.

The point $(-1,5)$ lies on the line, so its coordinates must satisfy the equation $y=-3x+b$.

Substitute $x=-1$ and $y=5$:

So the $y$-intercept of the line is $2$.

Now put $m=-3$ and $b=2$ into slope-intercept form $y=mx+b$:

This matches answer choice D, so the correct equation is $y=-3x+2$.