Compare the given slope $-\tfrac{3}{2}$ to the coefficient of $x$ in each answer choice. Which options can you eliminate immediately?

Take the remaining possibilities and plug in $x=6$ and $y=-1$. Which equation (or value of $b$ in $y=-\tfrac{3}{2}x+b$) makes the equation true?

In Desmos, enter each option on its own line: y = -3/2 x + 5, y = -2/3 x + 3, y = -2/3 x - 1, and y = -3/2 x + 8. You will see four different lines on the graph.

Type (6,-1) into Desmos to plot the point the line must pass through. Look at which of the four lines goes exactly through this point.

Among the lines that pass through $(6,-1)$, look at how steep they are: a slope of $-\tfrac{3}{2}$ means the line goes down 3 units for every 2 units you move to the right. Identify which graphed equation has this slope and passes through the point; that equation is the correct choice.

The slope–intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept. Here, the slope is given as $-\tfrac{3}{2}$, so any correct equation must have $m=-\tfrac{3}{2}$.

Look at each answer choice and identify the slope (the coefficient of $x$):

• A) slope $-\tfrac{3}{2}$
• B) slope $-\tfrac{2}{3}$
• C) slope $-\tfrac{2}{3}$
• D) slope $-\tfrac{3}{2}$

Since the line must have slope $-\tfrac{3}{2}$, choices B and C are impossible and can be eliminated. Only A and D remain.

Use the generic equation with the correct slope: $y=-\tfrac{3}{2}x+b$. Substitute the point $(6,-1)$ (so $x=6$ and $y=-1$):

Compute $-\tfrac{3}{2}\cdot 6=-9$, so the equation becomes

Add 9 to both sides: $b=8$. This means the $y$-intercept of line $r$ is 8.

We now know the line has slope $-\tfrac{3}{2}$ and $y$-intercept 8, so its equation in slope–intercept form is $y=-\tfrac{3}{2}x+8$. Among the answer choices, this is choice D.