The slope in slope-intercept form is directly identified as the coefficient of the 'x' variable.
Understanding Slope-Intercept Form
The slope-intercept form of a linear equation is a way to represent a line, and it is given by:
y = mx + b
Where:
- y is the dependent variable (usually plotted on the vertical axis)
- x is the independent variable (usually plotted on the horizontal axis)
- m represents the slope of the line. The slope describes the steepness and direction of the line.
- b represents the y-intercept, which is the point where the line crosses the y-axis.
Identifying the Slope
To find the slope (m) in a linear equation written in slope-intercept form, simply look at the coefficient of the x term. For example, in the equation y = -3x + 5, the slope is -3. As stated in the reference, in the equation y = − 3x + 5, the slope is − 3.
Here's how to find it:
- Look at the coefficient: In y = mx + b, 'm' is your slope.
- Example 1: If you have the equation y = 2x + 7, the slope is 2.
- Example 2: If you have the equation y = -5x - 3, the slope is -5.
- Example 3: If you have the equation y = x + 10, the slope is 1 (remember that if x stands alone, it is considered to have a coefficient of 1).
Practical Insights
- Positive slopes indicate that the line goes upwards from left to right.
- Negative slopes indicate that the line goes downwards from left to right.
- A zero slope indicates a horizontal line.
- The magnitude of the slope indicates the steepness of the line. A larger magnitude means a steeper line.
Table Summary
| Equation | Slope (m) | y-intercept (b) |
|---|---|---|
| y = 2x + 7 | 2 | 7 |
| y = -5x - 3 | -5 | -3 |
| y = x + 10 | 1 | 10 |
| y = -3x + 5 | -3 | 5 |
