Point Slope Form
y-y₁=m(x-x₁)
The point-slope form is a method of expressing a linear function. It is used to describe a line in Cartesian coordinates, specifying one point on the line and the slope of the line. The point-slope form is defined as:
y – y1 = m(x – x1),
where (x1, y1) is any point on the line and m is the slope of the line.
The point-slope form is useful when you need to find the equation of a line and you know one point on the line and the slope of the line. To use this form, you start with the given point (x1, y1) and the slope m and plug these values into the point-slope form equation. You can then simplify the equation to the slope-intercept form (y = mx + b) or any other form you need.
Example: Find the equation of the line passing through the point (3, 2) with a slope of 4.
Solution: Using the point-slope form, we have y – y1 = m(x – x1), where x1 = 3, y1 = 2, and m = 4. Substituting these values we get, y – 2 = 4(x – 3).
Simplifying further, we get y – 2 = 4x – 12
Therefore, the equation of the line passing through (3, 2) with a slope of 4 is y = 4x – 10 in the slope-intercept form.
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