The slope-intercept form of a linear equation is given by the formula:
\[ y = mx + b \]
where:
- \( y \) is the dependent variable (the output of the function),
- \( x \) is the independent variable (the input of the function),
- \( m \) is the slope of the line, which represents the rate of change of \( y \) with respect to \( x \),
- \( b \) is the y-intercept, which is the point where the line crosses the y-axis (when \( x = 0 \)).
Example
If you have the equation:
\[ y = 2x + 3 \]
In this case:
- The slope \( m \) is \( 2 \), meaning for every unit increase in \( x \), \( y \) increases by \( 2 \).
- The y-intercept \( b \) is \( 3 \), meaning the line crosses the y-axis at the point \( (0, 3) \).
Converting to Slope-Intercept Form
If you have an equation in another form, you can convert it to slope-intercept form. For example, if you have:
\[ 3x - 4y = 12 \]
To convert it, you would isolate \( y \):
-
Move \( 3x \) to the other side:
\[-4y = -3x + 12\] -
Divide by \(-4\):
\[y = \frac{3}{4}x - 3\]
Now, the equation is in slope-intercept form, where the slope \( m = \frac{3}{4} \) and the y-intercept \( b = -3 \).