Answered

Get the information you need from a community of experts on IDNLearn.com. Our platform is designed to provide quick and accurate answers to any questions you may have.

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 :

GinnyAnsweridn
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]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.