Lesson 18: Point-Slope Form of a Line
The point-slope form of a linear equation is used when you know the slope of a line and one point on the line. It is written as:
y - yâ‚ = m(x - xâ‚)
- (xâ‚, yâ‚) = a point on the line
- m = slope of the line
Examples
Example 1: Find the equation of a line with slope m = 2 passing through (3, 4)
- Use the formula: y - yâ‚ = m(x - xâ‚)
- y - 4 = 2(x - 3)
- Optionally, expand to slope-intercept form: y = 2x - 2
Example 2: Line with slope m = -1/2 through (2,5)
- y - 5 = -1/2(x - 2)
- Expanded: y = -1/2x + 6
Practice Problems
- Write the point-slope form for a line through (1,2) with slope 3.
- Convert y - 3 = 4(x - 1) into slope-intercept form.
- Write the equation of a line with slope -2 passing through (0,5).
- Graph y - 1 = 1/3(x - 3) using the point-slope method.
Lesson Summary
- Point-slope form: y - yâ‚ = m(x - xâ‚)
- Useful when you know a point and the slope.
- Can be converted to slope-intercept form for graphing.