Learn how to use the Point-Slope Form to quickly find the equation of a line in Cartesian coordinates

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.

More Answers:
Understanding Quadratic Equations: Real vs. Imaginary Solutions
Understanding Quadratic Equations: Finding Two Real and Distinct Roots Using Discriminant
Understanding the Discriminant in Quadratic Equations – Real and Complex Roots Explanation

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »