11. Graph the equation $$ -3 x+y=1 $$ Alope $$ = $$ -interospt =

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To graph the equation $$ -3x + y = 1 $$, we'll first rewrite it in **slope-intercept form**, which is $$ y = mx + b $$, where:
- $$ m $$ is the **slope**
- $$ b $$ is the **y-intercept**

### Step 1: Rewrite the Equation in Slope-Intercept Form

Start with the original equation:
$$
-3x + y = 1
$$

Solve for $$ y $$:
$$
y = 3x + 1
$$

### Step 2: Identify the Slope and Y-Intercept

From the rewritten equation $$ y = 3x + 1 $$:
- **Slope ($$ m $$):** 3
- **Y-Intercept ($$ b $$):** 1

So,
- **Slope = 3**
- **Y-Intercept = 1**

### Step 3: Graphing the Equation

1. **Plot the Y-Intercept:**
   - Start by plotting the y-intercept at $$ (0, 1) $$ on the graph.

2. **Use the Slope to Find Another Point:**
   - The slope $$ m = 3 $$ can be interpreted as the rise over run. This means you rise 3 units and run 1 unit to the right.
   - From $$ (0, 1) $$, move up 3 units to $$ (0, 1 + 3) = (0, 4) $$ and then 1 unit to the right to reach $$ (1, 4) $$.
   - Plot the point $$ (1, 4) $$.

3. **Draw the Line:**
   - Draw a straight line through the two points $$ (0, 1) $$ and $$ (1, 4) $$. This line represents the graph of the equation $$ y = 3x + 1 $$.

### Summary

- **Slope ($$ m $$) = 3**
- **Y-Intercept ($$ b $$) = 1**

### Graph Illustration

While I can't provide a visual graph here, following the steps above will allow you to accurately plot the line on graph paper or using graphing software.

**Example Points:**
- $$ (0, 1) $$ — Y-intercept
- $$ (1, 4) $$ — Using the slope
- You can add more points by continuing the pattern, such as $$ (2, 7) $$, $$ (-1, -2) $$, etc., to ensure the line is accurate.

**Final Equation:**
$$
y = 3x + 1
$$

This line has a positive slope, indicating that as $$ x $$ increases, $$ y $$ also increases.
To graph the equation $$ -3x + y = 1 $$, rewrite it as $$ y = 3x + 1 $$. The slope is 3 and the y-intercept is 1. Plot the point (0,1) and use the slope to find another point, such as (1,4). Draw a straight line through these points to graph the equation.

Graph the equation
Alope
-interospt =

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Graph the equation Alope -interospt =