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Equation of Line




 
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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.

    equation of a line

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.



How to Write Equations in Slope-Intercept Form

The slope-intercept from is useful when we want to find the slope or y-intercept of an equation. To write an equation in slope-intercept form, we isolate the y on one side of the equation.
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:

slope formula

Example:

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

Solution:

Step 1: Calculate the slope.

    slope = change in y / change in x= slope values

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: Substitute 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.
Example: Determine the equation of the line passing through (-2, -3) and (4, -2). Write the linear equation in slope-intercept form.
The following video shows more examples of getting the slope and y-intercept given two points and then obtaining the equation of the line.


How to graph an equation using the slope-intercept form

This video explains how to graph a linear equation given in slope intercept form.
The following video shows how to graph a linear equation using the slope and y-intercept.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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