Math worksheet for converting linear equations to function form and graphing them.

Let's solve each problem step by step.

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Problem 5: $3x + y = 5$

#### Step 1: Write in Function Form
We want to solve for $y$ in terms of $x$:
$$
3x + y = 5
$$
Subtract $3x$ from both sides:
$$
y = -3x + 5
$$

✔ Function Form: $y = -3x + 5$

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#### Step 2: Create a Table of Values

Use the function $y = -3x + 5$ and plug in values of $x$:

| $x$ | $y = -3x + 5$ | $y$ | $(x, y)$ |
|------|------------------|-------|-----------|
| -2 | $-3(-2) + 5 = 6 + 5 = 11$ | 11 | (-2, 11) |
| -1 | $-3(-1) + 5 = 3 + 5 = 8$ | 8 | (-1, 8) |
| 0 | $-3(0) + 5 = 0 + 5 = 5$ | 5 | (0, 5) |
| 1 | $-3(1) + 5 = -3 + 5 = 2$ | 2 | (1, 2) |
| 2 | $-3(2) + 5 = -6 + 5 = -1$ | -1 | (2, -1) |

✔ Completed table:

| $x$ | $y = -3x + 5$ | $y$ | $(x, y)$ |
|------|------------------|-------|-----------|
| -2 | $-3(-2) + 5$ | 11 | (-2, 11) |
| -1 | $-3(-1) + 5$ | 8 | (-1, 8) |
| 0 | $-3(0) + 5$ | 5 | (0, 5) |
| 1 | $-3(1) + 5$ | 2 | (1, 2) |
| 2 | $-3(2) + 5$ | -1 | (2, -1) |

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#### Step 3: Graph the Equation
Plot the points:
(-2, 11), (-1, 8), (0, 5), (1, 2), (2, -1)

Then draw a straight line through them. This is a linear graph with slope $-3$ and y-intercept $5$.

> 📌 Note: Since this is text-based, you would plot these on the grid provided.

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Problem 6: $4x + 4y = 8$

#### Step 1: Write in Function Form
Solve for $y$:
$$
4x + 4y = 8
$$
Divide every term by 4:
$$
x + y = 2
$$
Now solve for $y$:
$$
y = -x + 2
$$

✔ Function Form: $y = -x + 2$

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#### Step 2: Create a Table of Values

Use $y = -x + 2$:

| $x$ | $y = -x + 2$ | $y$ | $(x, y)$ |
|------|----------------|-------|-----------|
| -2 | $-(-2) + 2 = 2 + 2 = 4$ | 4 | (-2, 4) |
| -1 | $-(-1) + 2 = 1 + 2 = 3$ | 3 | (-1, 3) |
| 0 | $-(0) + 2 = 0 + 2 = 2$ | 2 | (0, 2) |
| 1 | $-(1) + 2 = -1 + 2 = 1$ | 1 | (1, 1) |
| 2 | $-(2) + 2 = -2 + 2 = 0$ | 0 | (2, 0) |

✔ Completed table:

| $x$ | $y = -x + 2$ | $y$ | $(x, y)$ |
|------|----------------|-------|-----------|
| -2 | $-(-2) + 2$ | 4 | (-2, 4) |
| -1 | $-(-1) + 2$ | 3 | (-1, 3) |
| 0 | $-(0) + 2$ | 2 | (0, 2) |
| 1 | $-(1) + 2$ | 1 | (1, 1) |
| 2 | $-(2) + 2$ | 0 | (2, 0) |

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#### Step 3: Graph the Equation
Plot the points:
(-2, 4), (-1, 3), (0, 2), (1, 1), (2, 0)

Draw a straight line through them. Slope = $-1$, y-intercept = 2.

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Problem 7: $3x - 2y = 6$

#### Step 1: Write in Function Form
Solve for $y$:
$$
3x - 2y = 6
$$
Subtract $3x$:
$$
-2y = -3x + 6
$$
Divide by $-2$:
$$
y = \frac{3}{2}x - 3
$$

✔ Function Form: $y = \frac{3}{2}x - 3$

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#### Step 2: Find Coordinates

Use $y = \frac{3}{2}x - 3$

| $x$ | $y = \frac{3}{2}x - 3$ | $y$ | $(x, y)$ |
|------|----------------------------|-------|-----------|
| -4 | $\frac{3}{2}(-4) - 3 = -6 - 3 = -9$ | -9 | (-4, -9) |
| -2 | $\frac{3}{2}(-2) - 3 = -3 - 3 = -6$ | -6 | (-2, -6) |
| 0 | $\frac{3}{2}(0) - 3 = 0 - 3 = -3$ | -3 | (0, -3) |
| 2 | $\frac{3}{2}(2) - 3 = 3 - 3 = 0$ | 0 | (2, 0) |
| 4 | $\frac{3}{2}(4) - 3 = 6 - 3 = 3$ | 3 | (4, 3) |

✔ Completed table:

| $x$ | $y = \frac{3}{2}x - 3$ | $y$ | $(x, y)$ |
|------|----------------------------|-------|-----------|
| -4 | $\frac{3}{2}(-4) - 3$ | -9 | (-4, -9) |
| -2 | $\frac{3}{2}(-2) - 3$ | -6 | (-2, -6) |
| 0 | $\frac{3}{2}(0) - 3$ | -3 | (0, -3) |
| 2 | $\frac{3}{2}(2) - 3$ | 0 | (2, 0) |
| 4 | $\frac{3}{2}(4) - 3$ | 3 | (4, 3) |

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✔ Final Answers Summary:

#### 5)
- Function Form: $y = -3x + 5$
- Table filled as shown above.

#### 6)
- Function Form: $y = -x + 2$
- Table filled as shown above.

#### 7)
- Function Form: $y = \frac{3}{2}x - 3$
- Table filled as shown above.

You can now use the tables to graph problems 5 and 6 on the coordinate planes provided.

Let me know if you'd like help plotting or sketching the graphs!