Let’s solve each problem step by step.
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Problem 1: y = -4x + 3
We need to fill in the table for x = 0, 1, 2, 3.
- When x = 0:
y = -4(0) + 3 = 0 + 3 =
3
- When x = 1:
y = -4(1) + 3 = -4 + 3 =
-1
- When x = 2:
y = -4(2) + 3 = -8 + 3 =
-5
- When x = 3:
y = -4(3) + 3 = -12 + 3 =
-9
Table completed:
| x | y |
|---|----|
| 0 | 3 |
| 1 | -1 |
| 2 | -5 |
| 3 | -9 |
To graph: Plot points (0,3), (1,-1), (2,-5), (3,-9) and draw a straight line through them.
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Problem 2: y = (2/3)x - 1
Given x values: -6, -3, 0, 3
- When x = -6:
y = (2/3)(-6) - 1 = -4 - 1 =
-5
- When x = -3:
y = (2/3)(-3) - 1 = -2 - 1 =
-3
- When x = 0:
y = (2/3)(0) - 1 = 0 - 1 =
-1
- When x = 3:
y = (2/3)(3) - 1 = 2 - 1 =
1
Table completed:
| x | y |
|----|----|
| -6 | -5 |
| -3 | -3 |
| 0 | -1 |
| 3 | 1 |
Graph: Plot (-6,-5), (-3,-3), (0,-1), (3,1) — they should lie on a straight line with slope 2/3.
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Problem 3: y = 2x
Given x = 0, 2, 4
- When x = 0:
y = 2(0) =
0
- When x = 2:
y = 2(2) =
4
- When x = 4:
y = 2(4) =
8
Table completed:
| x | y |
|---|---|
| 0 | 0 |
| 2 | 4 |
| 4 | 8 |
Graph: Plot (0,0), (2,4), (4,8) — straight line through origin with slope 2.
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Problem 4: y = 5 - (1/2)x
Given x = 2, 4, 6, 8
- When x = 2:
y = 5 - (1/2)(2) = 5 - 1 =
4
- When x = 4:
y = 5 - (1/2)(4) = 5 - 2 =
3
- When x = 6:
y = 5 - (1/2)(6) = 5 - 3 =
2
- When x = 8:
y = 5 - (1/2)(8) = 5 - 4 =
1
Table completed:
| x | y |
|---|---|
| 2 | 4 |
| 4 | 3 |
| 6 | 2 |
| 8 | 1 |
Graph: Plot (2,4), (4,3), (6,2), (8,1) — straight line sloping downward.
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All tables are now filled correctly. Graphs can be drawn by plotting these points and connecting them with straight lines since all equations are linear.
Final Answer:
The completed tables are:
1. For y = -4x + 3:
x=0 → y=3; x=1 → y=-1; x=2 → y=-5; x=3 → y=-9
2. For y = (2/3)x - 1:
x=-6 → y=-5; x=-3 → y=-3; x=0 → y=-1; x=3 → y=1
3. For y = 2x:
x=0 → y=0; x=2 → y=4; x=4 → y=8
4. For y = 5 - (1/2)x:
x=2 → y=4; x=4 → y=3; x=6 → y=2; x=8 → y=1
Parent Tip: Review the logic above to help your child master the concept of tables graphs and equations worksheet.
