Question 348·Easy·Algebra

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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	4
2	3

x	y
0	-5
1	-3
2	-1

x	y
0	0
1	2
2	4

x	y
0	5
1	3
2	1

An equation of the form $y=mx+b$ is a linear equation: $b$ gives the output at $x=0$ , and $m$ gives the change in $y$ each time $x$ increases by $1$ . For a matching-table question, define the rule in Desmos and evaluate the listed inputs. Check both the starting output and the change; one matching row may not be enough.

Hints

Hint 1
Each table row pairs an input $x$ with an output $y$ . Put the row’s $x$ into the given rule to find its output. Start with $x=0$ : which number does the rule give?
Hint 2
The slope is the change in $y$ when $x$ increases by $1$ . Read the coefficient of $x$ to find that change, then compare it with the change between rows in a table. Do they match?

Step-by-step

Evaluate the table inputs in Desmos
Step 1
Find the output at zero
Each row’s $x$ is the input, and $y$ is its output. Name the given rule $f(x)=-2x+5$ in Desmos, then type $f(0)$ . Desmos prints $5$ , so the table needs the row $(0,5)$ . Don’t stop at one row: more than one table can start there.
Step 2
Check the next output
Add $f(1)$ ; Desmos prints $3$ . The $-2$ in the rule is the slope: increasing $x$ by $1$ lowers $y$ by $2$ , from $5$ to $3$ . A table with $4$ at $x=1$ has the wrong change.
Step 3
Confirm the third row and choose the table
Add $f(2)$ ; Desmos prints $1$ . Keep each output with its input: the rows are $(0,5)$ , $(1,3)$ , and $(2,1)$ . That’s the table for the given equation. Choice D.

Question 348·Easy·Algebra

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Step-by-step

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