Find the slope and $$ y $$-intercept of the line. Graph the line. $$ 5 x+y=9 $$

Question

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To find the **slope** and **$$ y $$-intercept** of the line given by the equation:

$$
5x + y = 9
$$

follow these steps:

### 1. Rewrite the Equation in Slope-Intercept Form

The slope-intercept form of a linear equation is:

$$
y = mx + b
$$

where:
- $$ m $$ is the **slope**,
- $$ b $$ is the **$$ y $$-intercept**.

**Steps to Rearrange:**

1. Start with the original equation:
   $$
   5x + y = 9
   $$

2. Solve for $$ y $$:
   $$
   y = -5x + 9
   $$

### 2. Identify the Slope and $$ y $$-intercept

From the rearranged equation $$ y = -5x + 9 $$:

- **Slope ($$ m $$)**: The coefficient of $$ x $$ is **-5**.
  
  $$
  m = -5
  $$

- **$$ y $$-intercept ($$ b $$)**: The constant term is **9**.
  
  $$
  b = 9
  $$

### 3. Graphing the Line

To graph the line $$ y = -5x + 9 $$, follow these steps:

#### a. Plot the $$ y $$-intercept

- Start by plotting the $$ y $$-intercept at the point $$ (0, 9) $$ on the coordinate plane.

#### b. Use the Slope to Find Another Point

- **Slope ($$ m = -5 $$)** can be interpreted as the ratio $$ \frac{\text{rise}}{\text{run}} = \frac{-5}{1} $$.
  
  This means for every 1 unit you move **horizontally** to the right, you move **5 units down**.

- Starting from $$ (0, 9) $$, move 1 unit to the right and 5 units down to reach the point $$ (1, 4) $$.

#### c. Draw the Line

- Plot both points $$ (0, 9) $$ and $$ (1, 4) $$.
- Draw a straight line passing through these points, extending in both directions.

#### d. Optional: Plotting Another Point

- For better accuracy, plot a third point. For example, set $$ x = 2 $$:
  
  $$
  y = -5(2) + 9 = -10 + 9 = -1
  $$
  
  So, plot the point $$ (2, -1) $$.

### 4. Graph Illustration

Here's a simple representation of the graph:

```
y
|
10|           
9 |• (0,9)
8 |           
7 |           
6 |           
5 |           
4 |        • (1,4)
3 |           
2 |           
1 |           
0 |________________________ x
    0   1   2   3   4
```

*Note*: To fully visualize the graph, it's recommended to plot it on graph paper or using graphing software.

### Summary

- **Slope ($$ m $$)**: -5
- **$$ y $$-intercept ($$ b $$)**: 9

The line decreases steeply due to the negative slope, crossing the $$ y $$-axis at $$ (0, 9) $$ and passing through points like $$ (1, 4) $$ and $$ (2, -1) $$.
The slope of the line is -5 and the $$ y $$-intercept is 9. The line crosses the $$ y $$-axis at (0, 9) and decreases as $$ x $$ increases.

Find the slope and \( y \)-intercept of the line. Graph the line. \[ 5 x+y=9 \]

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