Graph and write a two-variable inequality

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Milo wants y alone in -3y > 6x - 9, with the same graph. Which inequality does that?

   • y < -2x + 3
   • y > -2x + 3
   • y < -2x - 9
   • y < -2x - 3
2. 2.

   Noah wants y alone in 6x + 3y < 12, with the same graph. Which inequality does that?

   • y > -2x + 4
   • y < -2x + 4
   • y < -2x + 12
   • y < 2x + 4
3. 3.

   Pia wants y alone in 5x + 5y ≥ 15, with the same graph. Which inequality does that?

   • y ≥ -x + 15
   • y ≤ -x + 3
   • y ≥ -x + 3
   • y ≥ x + 3

4. Read this first

   Boundary rows

   x	y
   0	4
   1	2
   2	0
   3	-2

5. 4.

   Ren fills a table for the boundary line. The line is dashed and the point (0, 0) is shaded. Which inequality fits?

   • y < 2x + 4
   • y < -2x + 4
   • y > -2x + 4
   • y ≤ -2x + 4
6. 5.

   Tala fills a table for the boundary line. The line is solid and the point (0, 0) is shaded. Which inequality fits?

   • y ≥ 3x
   • y ≥ 3x - 3
   • y > 3x - 3
   • y ≤ 3x - 3
7. 6.

   Zee fills a table for the boundary line. The line is solid and the point (1, 9) is shaded. Which inequality fits?

   • y ≤ 3x + 2
   • y ≥ 3x + 5
   • y ≥ 3x + 2
   • y > 3x + 2
8. 7.

   Ari fills a table for the boundary line. The line is dashed and the point (0, 0) is shaded. Which inequality fits?

   • y < 2x + 7
   • y < -2x + 7
   • y ≤ -2x + 7
   • y > -2x + 7
9. 8.

   Esme plots points with whole-number x and y, both at least 0. How many points make x + y ≤ 6 true?

   28
10. 9.

    Jun plots points with whole-number x and y, both at least 0. How many points make 3x + 2y < 13 true?

    19
11. 10.

    Kira plots points with whole-number x and y, both at least 0. How many points make x + 2y ≤ 8 true?

    25