Let’s solve each problem step by step.
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Problem 1: Is (4,3) a solution to 4x – 5y = 1?
Plug in x = 4 and y = 3 into the equation:
4*(4) – 5*(3) = 16 – 15 =
1
That matches the right side of the equation (which is 1). So yes, it works.
✔ Answer for #1:
Yes
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Problem 2: Is (4,4) a solution to 3y + x = 18?
Plug in x = 4 and y = 4:
3*(4) + 4 = 12 + 4 =
16
But the equation says it should equal 18. 16 ≠ 18 → Not a solution.
✘ Answer for #2:
No
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Problem 3: Graph y = x – 3 using table
We’ll plug in each x value into y = x – 3 to find y, then write the coordinate pair.
- When x = -2 → y = -2 – 3 =
-5 → (-2, -5)
- When x = -1 → y = -1 – 3 =
-4 → (-1, -4)
- When x = 0 → y = 0 – 3 =
-3 → (0, -3)
- When x = 1 → y = 1 – 3 =
-2 → (1, -2)
- When x = 2 → y = 2 – 3 =
-1 → (2, -1)
Now you can plot these points on the graph and draw a straight line through them.
📝 Table filled:
| x | y = x – 3 | y | (x, y) |
|----|-----------|-----|-----------|
| -2 | -2 – 3 | -5 | (-2, -5) |
| -1 | -1 – 3 | -4 | (-1, -4) |
| 0 | 0 – 3 | -3 | (0, -3) |
| 1 | 1 – 3 | -2 | (1, -2) |
| 2 | 2 – 3 | -1 | (2, -1) |
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Problem 4: Graph y = 2x + 4 using table
Plug in each x value:
- x = -2 → y = 2*(-2) + 4 = -4 + 4 =
0 → (-2, 0)
- x = -1 → y = 2*(-1) + 4 = -2 + 4 =
2 → (-1, 2)
- x = 0 → y = 2*0 + 4 = 0 + 4 =
4 → (0, 4)
- x = 1 → y = 2*1 + 4 = 2 + 4 =
6 → (1, 6)
- x = 2 → y = 2*2 + 4 = 4 + 4 =
8 → (2, 8)
Plot these points and connect with a straight line.
📝 Table filled:
| x | y = 2x + 4 | y | (x, y) |
|----|------------|-----|-----------|
| -2 | 2*(-2)+4 | 0 | (-2, 0) |
| -1 | 2*(-1)+4 | 2 | (-1, 2) |
| 0 | 2*0+4 | 4 | (0, 4) |
| 1 | 2*1+4 | 6 | (1, 6) |
| 2 | 2*2+4 | 8 | (2, 8) |
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Final Answer:
1) Yes
2) No
3) Table:
x=-2 → y=-5 → (-2,-5)
x=-1 → y=-4 → (-1,-4)
x=0 → y=-3 → (0,-3)
x=1 → y=-2 → (1,-2)
x=2 → y=-1 → (2,-1)
4) Table:
x=-2 → y=0 → (-2,0)
x=-1 → y=2 → (-1,2)
x=0 → y=4 → (0,4)
x=1 → y=6 → (1,6)
x=2 → y=8 → (2,8)
Parent Tip: Review the logic above to help your child master the concept of linear tables worksheet.
