Question 13 Graph the equation $$ -3 x+5 y=-5 $$ by writing the equation in the form $$ y=m x+b $$

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To graph the equation $$ -3x + 5y = -5 $$ by rewriting it in the slope-intercept form $$ y = mx + b $$, follow these steps:

## Step 1: Rewrite the Equation in $$ y = mx + b $$ Form

The slope-intercept form of a linear equation is:
$$ y = mx + b $$
where:
- $$ m $$ is the slope of the line.
- $$ b $$ is the y-intercept (the point where the line crosses the y-axis).

Let's manipulate the given equation to match this form.

### Given Equation:
$$ -3x + 5y = -5 $$

### Solve for $$ y $$:
1. **Add $$ 3x $$ to both sides:**
   $$ 5y = 3x - 5 $$

2. **Divide every term by 5 to isolate $$ y $$:**
   $$ y = \frac{3}{5}x - 1 $$

Now, the equation is in the slope-intercept form:
$$ y = \frac{3}{5}x - 1 $$

Here:
- **Slope ($$ m $$)** = $$ \frac{3}{5} $$
- **Y-intercept ($$ b $$)** = $$ -1 $$

## Step 2: Identify Key Components for Graphing

1. **Y-intercept ($$ b $$)**:
   - The y-intercept is $$ -1 $$, which means the line crosses the y-axis at the point $$ (0, -1) $$.

2. **Slope ($$ m $$)**:
   - The slope $$ \frac{3}{5} $$ indicates that for every 5 units moved horizontally (to the right), the line moves up 3 units vertically.

## Step 3: Plot the Points and Draw the Line

1. **Plot the Y-intercept ($$ 0, -1 $$):**
   - Start by placing a point at $$ (0, -1) $$ on the graph.

2. **Use the Slope to Find a Second Point:**
   - From $$ (0, -1) $$, move **5 units to the right** (positive direction of the x-axis) and **3 units up** (positive direction of the y-axis) to reach the point $$ (5, 2) $$.

3. **Plot the Second Point ($$ 5, 2 $$):**
   - Place a point at $$ (5, 2) $$.

4. **Draw the Line:**
   - Connect the two points with a straight line extending in both directions. This line represents the equation $$ y = \frac{3}{5}x - 1 $$.

## Visual Representation

Below is an ASCII representation of the graph:

```
y
|
3 +                         *
  |                        (5,2)
2 +
  |
1 +
  |
0 +---------*----------------- x
  |        (0,-1)
-1+
  |
```

- The point $$ (0, -1) $$ is the y-intercept.
- The point $$ (5, 2) $$ is another point on the line based on the slope.
- The line through these points represents the equation $$ y = \frac{3}{5}x - 1 $$.

## Conclusion

By rewriting the original equation in slope-intercept form, identifying the slope and y-intercept, plotting the corresponding points, and drawing the line through them, you've successfully graphed the equation $$ -3x + 5y = -5 $$.
To graph the equation $$ -3x + 5y = -5 $$, rewrite it as $$ y = \frac{3}{5}x - 1 $$. Plot the y-intercept at $$ (0, -1) $$ and use the slope $$ \frac{3}{5} $$ to find another point, such as $$ (5, 2) $$. Draw a straight line through these points to represent the equation.

Question 13 Graph the equation \( -3 x+5 y=-5 \) by writing the equation in the form \( y=m x+b \)

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