-(6-2)-point-slope-form.jpeg "(-6 6) (6 2) Point Slope Form")
Point Slope Form of a Linear Equation
In algebra, a linear equation can be expressed in various forms, including the point slope form. This form is particularly useful when we are given a point on a line and the slope of the line.
What is the Point Slope Form?
The point slope form of a linear equation is given by:
y - y1 = m(x - x1)
where:
- (x1, y1) is a point on the line
- m is the slope of the line
- x and y are the variables representing the x-coordinate and y-coordinate of any point on the line, respectively
How to Use the Point Slope Form
To use the point slope form, we need to know the coordinates of a point on the line and the slope of the line. Let's consider an example.
Example 1: Find the equation of the line that passes through the point (-6, 6) and has a slope of 6.
Using the point slope form, we can write the equation as:
y - 6 = 6(x - (-6))
Simplifying the equation, we get:
y - 6 = 6(x + 6)
y - 6 = 6x + 36
y = 6x + 42
Therefore, the equation of the line is y = 6x + 42.
Example 2: Find the equation of the line that passes through the point (6, 2) and has a slope of 2.
Using the point slope form, we can write the equation as:
y - 2 = 2(x - 6)
Simplifying the equation, we get:
y - 2 = 2x - 12
y = 2x - 10
Therefore, the equation of the line is y = 2x - 10.
Conclusion
The point slope form is a powerful tool for finding the equation of a line when we are given a point and the slope. By using this form, we can easily find the equation of a line and graph it on a coordinate plane.
