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]
