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# Graphing Linear Equations

Graphing linear equations is a way of visually representing the relationship between two variables.

• Graphing Linear Equations
• Solved Examples
• FAQs

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## Graphing Linear Equations

Graphing linear equations is a way of visually representing the relationship between two variables. In a linear equation, the variables are usually represented by x and y, and the equation takes the form:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). To graph a linear equation, follow these steps:

Determine the slope and y-intercept of the line. If the equation is not in slope-intercept form (y = mx + b), rearrange it to get it in that form.

Plot the y-intercept on the y-axis. This is the point (0, b).

Use the slope to find another point on the line. The slope represents the change in y over the change in x, so you can move up or down by the slope over one unit to the right to find another point on the line.

Draw a straight line connecting the two points. This line represents the graph of the linear equation. Here are some examples of graphing linear equations:

Example 1: Graph the equation y = 2x + 1.

Solution:

The slope of the line is 2, and the y-intercept is 1. To graph the equation, plot the y-intercept at the point (0, 1), and then use the slope to find another point on the line. Moving up by 2 units and to the right by 1 unit from the y-intercept gives the point (1, 3). Connect the two points with a straight line to get the graph of the equation:

<img src=”https://i.imgur.com/RmAlcvd.png” alt=”Graph of y = 2x + 1″>

Example 2: Graph the equation y = -3x + 4.

Solution:

The slope of the line is -3, and the y-intercept is 4. To graph the equation, plot the y-intercept at the point (0, 4), and then use the slope to find another point on the line. Moving down by 3 units and to the right by 1 unit from the y-intercept gives the point (1, 1). Connect the two points with a straight line to get the graph of the equation:

<img src=”https://i.imgur.com/36hCgtF.png” alt=”Graph of y = -3x + 4″>

Example 3: Graph the equation 2x – y = 6.

Solution:

To graph the equation, we first need to rearrange it into slope-intercept form (y = mx + b):

2x – y = 6

-y = -2x + 6

y = 2x – 6

The slope of the line is 2, and the y-intercept is -6. Plot the y-intercept at the point (0, -6), and then use the slope to find another point on the line. Moving up by 2 units and to the right by 1 unit from the y-intercept gives the point (1, -4). Connect the two points with a straight line to get the graph of the equation:

<img src=”https://i.imgur.com/6OajVNS.png” alt=”Graph of 2x – y = 6″>

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## Solved Examples

Example 1: Graph the equation y = 3x – 2.

Solution:

The slope of the line is 3, and the y-intercept is -2. To graph the equation, plot the y-intercept at the point (0, -2), and then use the slope to find another point on the line. Moving up by 3 units and to the right by 1 unit from the y-intercept gives the point (1, 1). Connect the two points with a straight line to get the graph of the equation:

<img src=”https://i.imgur.com/D7Cq3Jm.png” alt=”Graph of y = 3x – 2″>

Example 2: Graph the equation y = -1/2x + 4.

Solution:

The slope of the line is -1/2, and the y-intercept is 4. To graph the equation, plot the y-intercept at the point (0, 4), and then use the slope to find another point on the line. Moving down by 1 unit and to the right by 2 units from the y-intercept gives the point (2, 3). Connect the two points with a straight line to get the graph of the equation:

<img src=”https://i.imgur.com/dXYDKxN.png” alt=”Graph of y = -1/2x + 4″>

Example 3: Graph the equation y = 2.

Solution:

This equation represents a horizontal line passing through the point (0, 2). Since the slope of a horizontal line is 0, we don’t need to use the slope to find another point. The graph of the equation is just a horizontal line at y = 2:

<img src=”https://i.imgur.com/9OjFQ1W.png” alt=”Graph of y = 2″>

Example 4: Graph the equation 3x + 4y = 12.

Solution:

To graph the equation, we first need to rearrange it into slope-intercept form (y = mx + b):

3x + 4y = 12

4y = -3x + 12

y = (-3/4)x + 3

The slope of the line is -3/4, and the y-intercept is 3. Plot the y-intercept at the point (0, 3), and then use the slope to find another point on the line. Moving down by 3 units and to the right by 4 units from the x-intercept gives the point (4, 0). Connect the two points with a straight line to get the graph of the equation:

<img src=”https://i.imgur.com/xw3l6Dx.png” alt=”Graph of 3x + 4y = 12″>

Example 5: Graph the equation x = -2.

Solution:

This equation represents a vertical line passing through the point (-2, 0). Since the slope of a vertical line is undefined, we don’t need to use the slope to find another point. The graph of the equation is just a vertical line at x = -2:

<img src=”https://i.imgur.com/dQFv7jE.png” alt=”Graph of x = -2″>

## FAQS

##### What is the slope-intercept form of a linear equation?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

##### How do you find the slope of a line from an equation?

To find the slope of a line from an equation in slope-intercept form, simply look at the coefficient of x. For example, in the equation y = 2x + 3, the slope is 2.

##### How do you graph a linear equation?

To graph a linear equation, first find the y-intercept by identifying the value of y when x is 0. Then use the slope to find another point on the line, and connect the two points with a straight line.

##### What is a vertical line?

A vertical line is a line that runs up and down (perpendicular to the x-axis) and has an undefined slope. In an equation of the form x = a, where a is a constant, the graph is a vertical line passing through the point (a, 0).

##### What is a horizontal line?

A horizontal line is a line that runs left to right (parallel to the x-axis) and has a slope of 0. In an equation of the form y = b, where b is a constant, the graph is a horizontal line passing through the point (0, b).

##### How do you determine the x-intercept and y-intercept of a linear equation?

To find the x-intercept of a linear equation, set y equal to 0 and solve for x. To find the y-intercept, set x equal to 0 and solve for y. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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