Question 580·Medium·Algebra

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The inequality is

y \le -3x + 7

For which table are all the listed $(x,y)$ pairs solutions of the inequality?

x	y
2	2
1	5
0	8

x	y
2	4
-1	7
3	-3

x	y
2	1
0	7
3	-2

x	y
2	3
-1	10
4	-6

A two-variable inequality tells you which $(x,y)$ pairs make a comparison true; a table qualifies only if every row does. Graph the inequality in Desmos, then test rows that share an $x$ -value to rule out tables quickly. One failing row rules out an entire table. Remember that a solid boundary counts because the inequality allows equality.

Hints

Hint 1
An ordered pair $(x,y)$ puts $x$ first and $y$ second. Every table starts with $x=2$ , so compare those four $y$ -values with the height of the boundary at $x=2$ .
Hint 2
The boundary line is where $y=-3x+7$ . Desmos shades the points that satisfy $y\le-3x+7$ . Does a point exactly on the line count?
Hint 3
Passing the first row is not enough: a table needs every pair to work. Plot the other two pairs in the table that survives your first-row check.

Step-by-step

Graph the inequality and test the table rows
Step 1
See which points satisfy the inequality
Type $y\le-3x+7$ into Desmos. It shades the points on or below the boundary line, where $y=-3x+7$ . The boundary is solid, so points on it count: $\le$ means “less than or equal to.”
Step 2
Test the shared first-row value
Every table starts with $x=2$ , so plot its four first-row pairs: $(2,2)$ , $(2,4)$ , $(2,1)$ , and $(2,3)$ . Desmos shows $(2,1)$ on the boundary; the other three are above the shading. Their tables fail immediately, but the table starting with $(2,1)$ still needs its other rows checked.
Step 3
Check the remaining two rows
Plot the remaining pairs, $(0,7)$ and $(3,-2)$ . Desmos shows both on the solid boundary, so both satisfy the inequality. All three pairs in that table are solutions. Choice C.

Question 580·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this