QUESTION IMAGE
Question
- $y = -2x + 5$
| $x$ | $y$ |
|---|---|
| -1 | |
| 1 | |
| 3 | |
| 7 |
- $y = -\frac{4}{5}x + 1$
| $x$ | $y$ |
|---|---|
| -5 | |
| 0 | |
| 5 | |
| 10 |
- $y = -7 - x$
| $x$ | $y$ |
|---|---|
- $y = 5 - \frac{1}{4}x$
Problem 10: \( y = -2x + 5 \)
Step 1: Calculate \( y \) when \( x = -2 \)
Substitute \( x = -2 \) into \( y = -2x + 5 \):
\( y = -2(-2) + 5 = 4 + 5 = 9 \)
Step 2: Calculate \( y \) when \( x = -1 \)
Substitute \( x = -1 \) into \( y = -2x + 5 \):
\( y = -2(-1) + 5 = 2 + 5 = 7 \)
Step 3: Calculate \( y \) when \( x = 1 \)
Substitute \( x = 1 \) into \( y = -2x + 5 \):
\( y = -2(1) + 5 = -2 + 5 = 3 \)
Step 4: Calculate \( y \) when \( x = 3 \)
Substitute \( x = 3 \) into \( y = -2x + 5 \):
\( y = -2(3) + 5 = -6 + 5 = -1 \)
Step 5: Calculate \( y \) when \( x = 7 \)
Substitute \( x = 7 \) into \( y = -2x + 5 \):
\( y = -2(7) + 5 = -14 + 5 = -9 \)
Filled Table for Problem 10:
| \( x \) | \( y \) |
|---|---|
| -1 | 7 |
| 1 | 3 |
| 3 | -1 |
| 7 | -9 |
Problem 12: \( y = -\frac{4}{5}x + 1 \)
Step 1: Calculate \( y \) when \( x = -10 \)
Substitute \( x = -10 \) into \( y = -\frac{4}{5}x + 1 \):
\( y = -\frac{4}{5}(-10) + 1 = 8 + 1 = 9 \)
Step 2: Calculate \( y \) when \( x = -5 \)
Substitute \( x = -5 \) into \( y = -\frac{4}{5}x + 1 \):
\( y = -\frac{4}{5}(-5) + 1 = 4 + 1 = 5 \)
Step 3: Calculate \( y \) when \( x = 0 \)
Substitute \( x = 0 \) into \( y = -\frac{4}{5}x + 1 \):
\( y = -\frac{4}{5}(0) + 1 = 0 + 1 = 1 \)
Step 4: Calculate \( y \) when \( x = 5 \)
Substitute \( x = 5 \) into \( y = -\frac{4}{5}x + 1 \):
\( y = -\frac{4}{5}(5) + 1 = -4 + 1 = -3 \)
Step 5: Calculate \( y \) when \( x = 10 \)
Substitute \( x = 10 \) into \( y = -\frac{4}{5}x + 1 \):
\( y = -\frac{4}{5}(10) + 1 = -8 + 1 = -7 \)
Filled Table for Problem 12:
| \( x \) | \( y \) |
|---|---|
| -5 | 5 |
| 0 | 1 |
| 5 | -3 |
| 10 | -7 |
Problem 14: \( y = -7 - x \) (Let’s choose \( x = -2, -1, 0, 1, 2 \) to fill the table)
Step 1: Calculate \( y \) when \( x = -2 \)
Substitute \( x = -2 \) into \( y = -7 - x \):
\( y = -7 - (-2) = -7 + 2 = -5 \)
Step 2: Calculate \( y \) when \( x = -1 \)
Substitute \( x = -1 \) into \( y = -7 - x \):
\( y = -7 - (-1) = -7 + 1 = -6 \) (Wait, correction: \( -7 - (-1) = -7 + 1 = -6 \)? No, \( -7 - (-1) = -7 + 1 = -6 \)? Wait, no: \( -7 - (-1) = -7 + 1 = -6 \)? Wait, actually: \( -7 - (-1) = -6 \)? Wait, no, \( -7 + 1 = -6 \). Correct.
Step 3: Calculate \( y \) when \( x = 0 \)
Substitute \( x = 0 \) into \( y = -7 - x \):
\( y = -7 - 0 = -7 \)
Step 4: Calculate \( y \) when \( x = 1 \)
Substitute \( x = 1 \) into \( y = -7 - x \):
\( y = -7 - 1 = -8 \)
Step 5: Calculate \( y \) when \( x = 2 \)
Substitute \( x = 2 \) into \( y = -7 - x \):
\( y = -7 - 2 = -9 \)
Filled Table for Problem 14 (with \( x = -2, -1, 0, 1, 2 \)):
| \( x \) | \( y \) |
|---|---|
| -1 | -6 |
| 0 | -7 |
| 1 | -8 |
| 2 | -9 |
Problem 16: \( y = 5 - \frac{1}{4}x \) (Let’s choose \( x = -4, 0, 4, 8, 12 \) to fill the table)
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Step 1: Calculate \( y \) when \( x = -4 \)
Substitute \( x = -4 \) into \( y = 5 - \frac{1}{4}x \):
\( y = 5 - \frac{1}{4}(-4) = 5 + 1 = 6 \)
Step 2: Calculate \( y \) when \( x = 0 \)
Substitute \( x = 0 \) into \( y = 5 - \frac{1}{4}x \):
\( y = 5 - \frac{1}{4}(0) = 5 + 0 = 5 \)
Step 3: Calculate \( y \) when \( x = 4 \)
Substitute \( x = 4 \) into \( y = 5 - \frac{1}{4}x \):
\( y = 5 - \frac{1}{4}(4) = 5 - 1 = 4 \)
Step 4: Calculate \( y \) when \( x = 8 \)
Substitute \( x = 8 \) into \( y = 5 - \frac{1}{4}x \):
\( y = 5 - \frac{1}{4}(8) = 5 - 2 = 3 \)
Step 5: Calculate \( y \) when \( x = 12 \)
Substitute \( x = 12 \) into \( y = 5 - \frac{1}{4}x \):
\( y = 5 - \frac{1}{4}(12) = 5 - 3 = 2 \)
Filled Table for Problem 16 (with \( x = -4, 0, 4, 8, 12 \)):
| \( x \) | \( y \) |
|---|---|
| 0 | 5 |
| 4 | 4 |
| 8 | 3 |
| 12 | 2 |