Slope Intercept Form: How to Find the Equation of a Line Given a Point and Slope

Understanding the slope intercept form of a line is fundamental in geometry and algebra. This form allows us to easily identify key features of a line such as its slope and y-intercept. This article will guide you through the process of finding the equation of a line given a point and the slope.

What is the Slope Intercept Form?

The slope intercept form of a line is given by the equation:

y mx b

Here:

m represents the slope of the line. b is the y-intercept, the point where the line crosses the y-axis.

Finding the Equation of a Line with Given Point and Slope

Let's explore a step-by-step method to find the equation of a line when given a point and the slope.

Example 1: Line with Slope -2 Passing Through Point (-1, 3)

Given that a line has a slope of -2 and passes through the point (-1, 3), we need to find its equation in slope intercept form.

Start with the point-slope form of the equation of a line:

y - y1 m(x - x1)

Substituting the coordinates of the given point (-1, 3) and the slope (m -2), we get:

y - 3 -2(x - (-1))

Which simplifies to:

y - 3 -2(x 1)

Expand and rearrange the equation to put it in slope intercept form:

y - 3 -2x - 2

y -2x - 2 3

y -2x 1

The y-intercept (b) is 1, and the slope (m) is -2. Therefore, the equation of the line in slope intercept form is:

y -2x 1

Example 2: Line with Slope 2 Passing Through Point (-1, 3)

In this example, we are given a line with a slope of 2 that passes through the point (-1, 3). Follow the same process as in the previous example:

Write the point-slope form using the given slope (m 2) and point (-1, 3):

y - 3 2(x - (-1))

Which simplifies to:

y - 3 2(x 1)

Expand and rearrange the equation:

y - 3 2x 2

y 2x 2 3

y 2x 5

The y-intercept (b) is 5, and the slope (m) is 2. Therefore, the equation of the line in slope intercept form is: