Explanation:
The point-slope form and the slope-intercept form are two different forms of linear equations used in mathematics.
1. **Point-Slope Form:**
The point-slope form of a linear equation is given by:
\[y - y_1 = m(x - x_1)\]
Where:
- \((x_1, y_1)\) is a point on the line.
- \(m\) is the slope of the line.
This form is useful when you know a point on the line and its slope, and you want to write the equation of the line.
2. **Slope-Intercept Form:**
The slope-intercept form of a linear equation is given by:
\[y = mx + b\]
Where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept, which is the point where the line crosses the y-axis.
This form is particularly useful because it directly provides the slope and y-intercept of the line. It's often used when you know the slope and the y-intercept, or when you want to graph a line.
In summary, the point-slope form emphasizes a specific point and the slope, while the slope-intercept form emphasizes the slope and the y-intercept of a linear equation. Both forms are important tools in working with linear equations and lines.