The point-slope formula is used in coordinate geometry to find the equation of a line when you know the slope of the line and the coordinates of a point on the line. This formula is especially useful for writing the equation of a line in a quick and straightforward manner.
Point-Slope Formula
The point-slope formula is expressed as y – y1 = m(x – x1), where:
- ‘m’ is the slope of the line.
- (x1, y1) are the coordinates of a known point on the line.
- (x, y) are the coordinates of any other point on the line.
How to Use the Point-Slope Formula
- Start with the slope of the line and the coordinates of a known point on the line.
- Substitute the slope (m) and the coordinates of the known point (x1, y1) into the formula.
- Rearrange the formula to solve for y, if needed, to get the equation in slope-intercept form (y = mx + b).
Example 1
Write the equation of the line with a slope of 2 that passes through the point (3, 4).
Using the point-slope formula: y – 4 = 2(x – 3). This can be simplified to y = 2x – 2.
Example 2
Write the equation of the line with a slope of -1 that passes through the point (-2, 5).
Using the point-slope formula: y – 5 = -1(x + 2). This can be simplified to y = -x + 3.
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