Slope-Intercept Form from 2 Points Calculator: A Comprehensive Guide

The point-slope form is a powerful technique used to find the equation of a straight line, given two points on the line. However, sometimes it's more convenient to rewrite this equation in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. In this article, we'll explore how to convert point-slope form into slope-intercept form using a calculator or by hand.

Why Use Slope-Intercept Form?

The slope-intercept form is particularly useful when you need to highlight the slope and y-intercept of a line. This form emphasizes these key elements, making it easier to understand and work with linear equations. By contrast, point-slope form focuses on the slope and a point on the line that is not the y-intercept.

Step-by-Step Conversion

To convert point-slope form into slope-intercept form, follow these steps:

1. Start with the point-slope equation: y - y1 = m(x - x1)

2. Multiply both sides of the equation by (x - x1) to eliminate the term: y - y1 = m(x - x1)(x - x1)

3. Expand and simplify the right-hand side of the equation: y - y1 = mx - mx1 + y1

4. Add y1 to both sides of the equation to isolate y: y = mx - mx1 + y1

Example 1: Finding Slope-Intercept Form for a Negative Coordinate Point

Suppose we need to find the slope-intercept form of a line that passes through the points (-13, -12) and has a slope of 3.5. Following the steps above, we can substitute the values into the point-slope equation: y - (-12) = 3.5(x - (-13))

Example 2: Finding Slope-Intercept Form for a Positive Coordinate Point

For a positive coordinate point (3, 5), if the slope is 4, we can use the same steps to find the slope-intercept form: y - 5 = 4(x - 3)

Using Online Calculators

If you're short on time or prefer a more straightforward approach, you can use an online calculator like our point-slope form calculator. Simply enter the values for X and Y co-ordinates for two points, and the calculator will generate the linear equation in slope-intercept form.

In conclusion, converting point-slope form into slope-intercept form is a simple yet powerful technique that can help you better understand and work with linear equations. By following the steps outlined above or using an online calculator, you can easily find the slope-intercept form of a line given two points on the line. Whether you're working with negative or positive coordinate points, this method provides a convenient way to highlight the slope and y-intercept of a line.

References

Slope intercept form from 2 points calculator