Use any two points from the table and apply the slope formula $m=\dfrac{y_2-y_1}{x_2-x_1}$. This will help you quickly rule out some choices based on their slopes.

Once you know the slope $m$, plug in $x$ and $y$ from one of the table points into $y=mx+b$ to solve for $b$, the $y$-intercept.

After you find $m$ and $b$, compare with each equation option, or plug in one of the table $x$-values into each choice to see which gives the correct $y$.

Create a table in Desmos and enter the three points from the problem: $(1,17)$, $(4,11)$, and $(10,-1)$. You should see these three points plotted.

On separate lines, type each option exactly as given: y = -2x + 19, y = 2x + 19, y = -2x - 19, and y = -1/2x + 19. Desmos will draw four different lines.

Look at the graph and identify which of the four lines goes through all three plotted points. The corresponding equation is the correct choice.

For extra confirmation, click the gear icon next to each equation and add a table. Check the $y$-values in each line’s table for $x=1$, $x=4$, and $x=10$, and see which one matches the original table exactly.

Look at how $y$ changes as $x$ increases:

• From $x=1$ to $x=4$, $x$ increases by $3$, while $y$ changes from $17$ to $11$, a decrease of $6$.
• From $x=4$ to $x=10$, $x$ increases by $6$, while $y$ changes from $11$ to $-1$, a decrease of $12$.

So as $x$ increases, $y$ decreases, meaning the line must have a negative slope.

Use the slope formula with any two points, for example $(1,17)$ and $(4,11)$:

So the slope of the line is $m=-2$.

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

We know $m=-2$, and we can use a point from the table, say $(1,17)$, to find $b$:

Solve this equation for $b$.

Continue solving:

So the line has slope $-2$ and $y$-intercept $19$, which means its equation is $y=-2x+19$. Among the answer choices, this matches choice A.