Question
Which equation is written in slope-intercept form?
y = 3 x minus 2
x = one-half y + 8
2 x + 5 y = 12
3 y = 8 x minus 5
y = 3 x minus 2
x = one-half y + 8
2 x + 5 y = 12
3 y = 8 x minus 5
Answers
GPT-4o mini
The slope-intercept form of a linear equation is given by the formula:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Let's evaluate the given equations:
1. **\( y = 3x - 2 \)**: This is already in slope-intercept form with \( m = 3 \) and \( b = -2 \).
2. **\( x = \frac{1}{2}y + 8 \)**: This is not in slope-intercept form. To put it in that form, you would need to solve for \( y \).
3. **\( 2x + 5y = 12 \)**: This is not in slope-intercept form. To convert it, you would need to isolate \( y \).
4. **\( 3y = 8x - 5 \)**: This is not in slope-intercept form yet, but you can convert it by dividing the entire equation by 3 to isolate \( y \).
Thus, the equation that is already written in slope-intercept form is:
**\( y = 3x - 2 \)**.
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Let's evaluate the given equations:
1. **\( y = 3x - 2 \)**: This is already in slope-intercept form with \( m = 3 \) and \( b = -2 \).
2. **\( x = \frac{1}{2}y + 8 \)**: This is not in slope-intercept form. To put it in that form, you would need to solve for \( y \).
3. **\( 2x + 5y = 12 \)**: This is not in slope-intercept form. To convert it, you would need to isolate \( y \).
4. **\( 3y = 8x - 5 \)**: This is not in slope-intercept form yet, but you can convert it by dividing the entire equation by 3 to isolate \( y \).
Thus, the equation that is already written in slope-intercept form is:
**\( y = 3x - 2 \)**.