Question
How to write an equation in intercept slope line
Answers
Answered by
GPT-4o mini
To write an equation in slope-intercept form, you'll want to use the format:
\[ y = mx + b \]
where:
- \( y \) is the dependent variable.
- \( m \) is the slope of the line (how much \( y \) changes for a one-unit increase in \( x \)).
- \( x \) is the independent variable.
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0\)).
### Steps to Write an Equation in Slope-Intercept Form:
1. **Identify the Slope (m)**: This is often given or can be calculated from two points on the line. If you have two points, \( (x_1, y_1) \) and \( (x_2, y_2) \), the slope \( m \) can be calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
2. **Identify the Y-Intercept (b)**: The y-intercept is where the line crosses the y-axis. If it's not explicitly given, you can find it by substituting the slope and one point into the equation \( y = mx + b \) and solving for \( b \).
3. **Write the Equation**: Once you have both \( m \) and \( b \), substitute them into the slope-intercept form \( y = mx + b \).
### Example:
Suppose you have a slope of 3 and a y-intercept of -2.
1. Slope \( m = 3 \)
2. Y-Intercept \( b = -2 \)
Putting these values into the slope-intercept form gives:
\[
y = 3x - 2
\]
### Conclusion:
This is the equation of the line in slope-intercept form. Remember, if you start with two points, always calculate the slope first, then find the y-intercept before writing the final equation.
\[ y = mx + b \]
where:
- \( y \) is the dependent variable.
- \( m \) is the slope of the line (how much \( y \) changes for a one-unit increase in \( x \)).
- \( x \) is the independent variable.
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0\)).
### Steps to Write an Equation in Slope-Intercept Form:
1. **Identify the Slope (m)**: This is often given or can be calculated from two points on the line. If you have two points, \( (x_1, y_1) \) and \( (x_2, y_2) \), the slope \( m \) can be calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
2. **Identify the Y-Intercept (b)**: The y-intercept is where the line crosses the y-axis. If it's not explicitly given, you can find it by substituting the slope and one point into the equation \( y = mx + b \) and solving for \( b \).
3. **Write the Equation**: Once you have both \( m \) and \( b \), substitute them into the slope-intercept form \( y = mx + b \).
### Example:
Suppose you have a slope of 3 and a y-intercept of -2.
1. Slope \( m = 3 \)
2. Y-Intercept \( b = -2 \)
Putting these values into the slope-intercept form gives:
\[
y = 3x - 2
\]
### Conclusion:
This is the equation of the line in slope-intercept form. Remember, if you start with two points, always calculate the slope first, then find the y-intercept before writing the final equation.