Which table gives three values of and their corresponding values of for the given equation?

Solution available with step-by-step explanation

SAT Linear Equations in Two Variables Question 46 | Free SAT Prep | Aniko

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Question 46·Easy·Linear Equations in Two Variables

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y = -4x + 6

Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?

x	y
0	-6
2	-2
4	-14

For questions that ask which table matches an equation, quickly plug each given $x$ -value from the tables into the equation and compute $y$ by hand. Often you can eliminate several choices just by checking one easy value like $x=0$ , then use one more $x$ -value to distinguish between the remaining options. This is faster and less error-prone than trying to reason from the graph or from the slope and intercept alone.

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Click me!

Think about how to use the equation

The equation $y=-4x+6$ gives you a rule to find $y$ from $x$ . How can you use this rule for each $x$ -value shown in the tables?

Start with one easy $x$ -value

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

Check more than one row

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.

Desmos Guide

Graph the equation

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

Use a table to generate values

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.

Match with the answer choices

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.

Step-by-step Explanation

Understand what the equation tells you

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 $y$ .

Find $y$ when $x=0$

Substitute $x=0$ into the equation:

y = -4(0) + 6 = 0 + 6 = 6

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

Find $y$ when $x=2$

Substitute $x=2$ into the equation:

y = -4(2) + 6 = -8 + 6 = -2

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

Find $y$ when $x=4$

Substitute $x=4$ into the equation:

y = -4(4) + 6 = -16 + 6 = -10

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

Match your ordered pairs to a table

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:

x	y
0	6
2	-2
4	-10

So the correct answer is choice D.

Study Hints

Hints

Click me!

Think about how to use the equation

The equation $y=-4x+6$ gives you a rule to find $y$ from $x$ . How can you use this rule for each $x$ -value shown in the tables?

Start with one easy $x$ -value

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

Check more than one row

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.

Desmos Guide

Graph the equation

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

Use a table to generate values

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.

Match with the answer choices

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.

Step-by-step Explanation

Understand what the equation tells you

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 $y$ .

Find $y$ when $x=0$

Substitute $x=0$ into the equation:

y = -4(0) + 6 = 0 + 6 = 6

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

Find $y$ when $x=2$

Substitute $x=2$ into the equation:

y = -4(2) + 6 = -8 + 6 = -2

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

Find $y$ when $x=4$

Substitute $x=4$ into the equation:

y = -4(4) + 6 = -16 + 6 = -10

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

Match your ordered pairs to a table

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:

x	y
0	6
2	-2
4	-10

So the correct answer is choice D.

Strategy

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Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation