Equation of a line - Slope-Intercept Form

In this lesson, we will learn

• the slope-intercept form for the equation of a line.
• how to write equations in slope-intercept form.
• how to write equations of horizontal and vertical lines.
• how to get the equation of a line given two points on the line.
• how to graph an equation using the slope-intercept form.

Slope-Intercept Form

The equation, y = mx + b, is in slope-intercept form for the equation of a line. When an equation is in this form, the slope of the line is given by m and the y-intercept is located at b.

For example, a line with the equation y = 2x + 4 has a slope of 2 and a y-intercept of 4.

The following video gives an intuition of the slope and y-intercept of an equation.

Writing Equations in Slope-Intercept Form

The following video shows how to change a linear equation into slope-intercept form.

The following video shows how to find the slope and y-intercept of line by writing the equation in slope-intercept form.

The following video shows how to find the slope and y-intercept for a linear equation.

Equations of Horizontal and Vertical Lines

A horizontal line has a slope of zero which means that m = 0. The equation of a horizontal line is then in the form

y = 0x + b which is the same as y = b, where b is the y-intercept.

A vertical line has a slope that is undefined. Therefore, it cannot be written in slope-intercept form. Instead, the equation of a vertical line is in the form

x = a, where a is the x-intercept.

The following video shows how to write the equation of vertical and horizontal lines.

Writing the Equation of a Line from Two Points

To find the equation of a line when given two points on the line, we first find the slope and then find the y-intercept.

The slope is the ratio of the change in the y-value over the change in the x-value. Given any two points on a line, you can calculate the slope of the line by using this formula:

Example:

Given two points, P = (0, –1) and Q = (4,1), on the line, find the eqaution of the line.

Solution:

    slope = =

Step 2: Substitute m = , into the equation, y = mx + b, to get the equation

Step 3: Select one of the given points, for example (4, 1), and substitute the x and y values into the equation.

We, then, get that b = −1, which is the y-intercept.

Step 4: Subtitute b = −1 to get the equation.

y = x − 1

This video provides an example of how to determine the equation of a line in slope-intercept form given two points on the line. 

The following video shows more examples of getting the slope and y-intercept given two points and then obtaining the equation of the line.

 

 

Graph an equation using the slope-intercept form

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