# Equation of Line

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More Lessons for Geometry,

Math Worksheets
### 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* = 2*x* + 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* = 0*x* + *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 equation of the line.

*Solution: *

**Step 1:** Calculate the slope.

*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: **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.

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