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

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.
A linear equation written in the form y = mx + b is in slope intercept form where m is the slope and b is the y intercept of the line.
Example:
Write the equation -3x + 4y = 8 in slope intercept form. State the slope and y intercept.
How to find the slope and y-intercept of line by writing the equation in slope-intercept form?
Examples:
Find the slope:
y = -3x + 8
3x - 5y = 10
y = 5
x = -2
How to find the slope and y-intercept for a linear equation?
Examples:
Find the slope and y-intercept for the linear equation.
a) y = -2x + 3
b) y = 4 - 2/3 x
c) 2x - 5y = 10
d) 3x + 7y - 10 = 0
e) 8y + 24 = 0

### 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.

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

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.
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.
Example:
Identify the slope and y-intercept. Graph.
a) y = -2/3 x + 1
b) y = 5x - 2
c) y = x
d) 3x - 2y = 8
How to graph a linear equation using the slope and y-intercept?
Examples:
1. Graph the line y = -2/3 x + 4
2. Graph the line y = 3x + 2

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