Point Slope Formula For a Line
The Point Slope formula is used to write the equation of a straight line when you know the coordinates of a point on the line and the slope of the line
The Point Slope formula is used to write the equation of a straight line when you know the coordinates of a point on the line and the slope of the line. It is one of the most commonly used methods to express the equation of a line because it is straightforward and easy to use.
The Point Slope formula can be stated as:
y – y1 = m(x – x1)
Here’s what each part of the formula represents:
– (x1, y1): The coordinates of a point on the line. These values are used as the given point to construct the equation.
– m: The slope of the line. Slope measures the steepness or inclination of a line and is represented by the ratio of the vertical change (rise) to the horizontal change (run). The slope (m) is required to determine the equation of the line.
To use the Point Slope formula, follow these steps:
1. Identify a point that lies on the line. This point will be represented by (x1, y1).
2. Determine the slope (m) of the line using any given information, such as the slope of a line passing through two given points or the slope-intercept form of a line.
3. Substitute the values of (x1, y1) and m into the formula: y – y1 = m(x – x1).
4. Simplify the equation if needed.
5. This resulting equation is the equation of the line in the point-slope form.
Note: The Point Slope form can be converted to other forms, such as slope-intercept form or standard form, if required.
For example, let’s use the Point Slope formula to find the equation of a line passing through the point (2,4) with a slope of 3. Using the formula, we have:
y – 4 = 3(x – 2)
Simplifying this equation would give us the equation of the line in point-slope form.
In summary, the Point Slope formula is a helpful tool for finding the equation of a line when given a point on the line and the slope of the line. It provides a simple and concise way to express the equation of a line and is widely used in various applications in mathematics and physics.
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