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 70 | Free SAT Prep | Aniko

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Question 70·Easy·Linear Equations in Two Variables

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$y = -2x + 5$
Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?

x	y
0	-5
1	-3
2	-1

x	y
0	0
1	2
2	4

For questions asking which table matches a linear equation, quickly plug in the $x$ -values from the tables into the equation and compute the corresponding $y$ -values. Start with easy values like $x=0$ to find the $y$ -intercept, then check one or two more $x$ -values; eliminate any table where the $y$ -values do not match your calculations, focusing on both the starting value and how $y$ changes as $x$ increases.

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Start with $x=0$

If $x=0$ , the equation becomes $y=-2(0)+5$ . What is $y$ ? Then look for the table(s) that have that same $y$ -value when $x=0$ .

Check how $y$ changes when $x$ increases by 1

Because the equation is $y=-2x+5$ , each time $x$ increases by 1, $y$ should change by $-2$ . Look down the $y$ -column in each table and see which one shows that change.

Verify with substitution

Take $x=1$ and $x=2$ and plug them into $y=-2x+5$ . Then compare the $y$ -values you get to the $y$ -values in each table for those $x$ -values.

Desmos Guide

Graph the equation

In Desmos, type the equation $y=-2x+5$ on a new line so the line appears on the graph.

Create a table of values

Click the gear or plus icon next to the equation and choose the option to create a table (or add a separate table and label the columns $x$ and $y$ ).

Enter the given $x$ -values and read the $y$ -values

In the $x$ -column of the table, enter 0, 1, and 2. Desmos will automatically fill in the corresponding $y$ -values from the equation. Compare those three $(x,y)$ pairs with the answer choices to see which table matches.

Step-by-step Explanation

Understand what the equation tells you

The equation $y=-2x+5$ means: to get $y$ , multiply $x$ by $-2$ and then add 5. So for any $x$ -value in a table, you can compute the matching $y$ -value with this rule.

Find $y$ when $x=0$

Substitute $x=0$ into the equation $y=-2x+5$ : $y=-2(0)+5=0+5=5$ . So when $x=0$ , $y$ must be 5. Eliminate any table whose first row does not have $x=0$ paired with $y=5$ .

Find $y$ when $x=1$

Now substitute $x=1$ : $y=-2(1)+5=-2+5=3$ . So when $x=1$ , $y$ must be 3. Check which remaining table(s) have $x=1$ paired with $y=3$ .

Find $y$ when $x=2$ and match the table

Finally, substitute $x=2$ : $y=-2(2)+5=-4+5=1$ . So the correct three pairs are $(0,5)$ , $(1,3)$ , and $(2,1)$ , which matches the table

x	y
0	5
1	3
2	1

This is answer choice D.

Study Hints

Hints

Click me!

Start with $x=0$

If $x=0$ , the equation becomes $y=-2(0)+5$ . What is $y$ ? Then look for the table(s) that have that same $y$ -value when $x=0$ .

Check how $y$ changes when $x$ increases by 1

Because the equation is $y=-2x+5$ , each time $x$ increases by 1, $y$ should change by $-2$ . Look down the $y$ -column in each table and see which one shows that change.

Verify with substitution

Take $x=1$ and $x=2$ and plug them into $y=-2x+5$ . Then compare the $y$ -values you get to the $y$ -values in each table for those $x$ -values.

Desmos Guide

Graph the equation

In Desmos, type the equation $y=-2x+5$ on a new line so the line appears on the graph.

Create a table of values

Click the gear or plus icon next to the equation and choose the option to create a table (or add a separate table and label the columns $x$ and $y$ ).

Enter the given $x$ -values and read the $y$ -values

Step-by-step Explanation

Understand what the equation tells you

The equation $y=-2x+5$ means: to get $y$ , multiply $x$ by $-2$ and then add 5. So for any $x$ -value in a table, you can compute the matching $y$ -value with this rule.

Find $y$ when $x=0$

Substitute $x=0$ into the equation $y=-2x+5$ : $y=-2(0)+5=0+5=5$ . So when $x=0$ , $y$ must be 5. Eliminate any table whose first row does not have $x=0$ paired with $y=5$ .

Find $y$ when $x=1$

Now substitute $x=1$ : $y=-2(1)+5=-2+5=3$ . So when $x=1$ , $y$ must be 3. Check which remaining table(s) have $x=1$ paired with $y=3$ .

Find $y$ when $x=2$ and match the table

Finally, substitute $x=2$ : $y=-2(2)+5=-4+5=1$ . So the correct three pairs are $(0,5)$ , $(1,3)$ , and $(2,1)$ , which matches the table

x	y
0	5
1	3
2	1

This is answer choice D.

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation