Question 46·Easy·Linear Equations in Two Variables

Try substituting $x=0$ into $y=-4x+6$. What $y$-value do you get, and which answer choices have that $y$-value when $x=0$?

After you use one $x$-value to eliminate some choices, use another $x$-value (like 2 or 4) to see which remaining table matches the equation for all the given $x$-values.

In Desmos, type y = -4x + 6 to graph the line that represents the equation.

Click the plus (+) icon and choose "Table". In the $x$-column, enter the values 0, 2, and 4. Desmos will automatically fill in the corresponding $y$-values from the equation.

Look at the $(x,y)$ pairs shown in the Desmos table for $x=0$, $2$, and $4$. Compare those three pairs to each answer choice and select the table that lists exactly the same pairs in each row.

The equation $y=-4x+6$ means that for any value of $x$, you multiply $x$ by $-4$ and then add $6$ to get the corresponding $y$.

So to fill in a table, you will plug in each given $x$-value and calculate $y$.

Substitute $x=0$ into the equation:

So when $x=0$, the correct table must have $y=6$ in that row.

Substitute $x=2$ into the equation:

So when $x=2$, the correct table must have $y=-2$ in that row.

Substitute $x=4$ into the equation:

So when $x=4$, the correct table must have $y=-10$ in that row.

From the calculations, the correct $(x,y)$ pairs are $(0,6)$, $(2,-2)$, and $(4,-10)$. The only table that lists exactly these three pairs is:

So the correct answer is choice D.