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Order the steps to correctly change the equation from Standard Form to Slope-Intercept Form.

START: Standard Form
1. Add [tex]$x$[/tex] to both sides: [tex]$\quad -x + \frac{1}{3} y = \frac{1}{3}$[/tex]
2. [tex]$\quad \frac{1}{3} y = x + \frac{1}{3}$[/tex]
3. Multiply both sides by 3: [tex]$\quad y = 3x + 1$[/tex]

END: Slope-Intercept Form

After you have correctly ordered the steps, use the slope-intercept form equation to answer these questions:

The slope is: [tex]$\square$[/tex]

The [tex]$y$[/tex]-intercept is: [tex]$\square$[/tex]

Sagot :

GinnyAnswer
To convert the given equation from Standard Form to Slope-Intercept Form, follow these steps in the correct order:

### Standard Form to Slope-Intercept Form Conversion Steps:

1. Start with the given equation in Standard Form:
[tex]\[-x + \frac{1}{3}y = \frac{1}{3}\][/tex]

2. Add [tex]\(x\)[/tex] to both sides:
[tex]\[-x + \frac{1}{3}y + x = \frac{1}{3} + x\][/tex]
[tex]\[\frac{1}{3}y = x + \frac{1}{3}\][/tex]

3. Multiply both sides by 3 to eliminate the fraction:
[tex]\[3 \cdot \frac{1}{3}y = 3 \cdot (x + \frac{1}{3})\][/tex]
[tex]\[y = 3x + 1\][/tex]

### Correct Order of Steps:

1. Start with the equation in Standard Form:
[tex]\[-x + \frac{1}{3} y = \frac{1}{3}\][/tex]

2. Add [tex]\(x\)[/tex] to both sides:
[tex]\[\frac{1}{3} y = x + \frac{1}{3}\][/tex]

3. Multiply both sides by 3:
[tex]\[y = 3x + 1\][/tex]

### Slope-Intercept Form:

The equation in Slope-Intercept Form is:
[tex]\[y = 3x - 1\][/tex]

### Use the Slope-Intercept Form equation to find the slope and y-intercept:

The slope (m) is:
[tex]\[3\][/tex]

The y-intercept (b) is:
[tex]\[-1\][/tex]

Therefore:

- The slope is: [tex]\(\boxed{3}\)[/tex]
- The y-intercept is: [tex]\(\boxed{-1}\)[/tex]
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