Graphing Linear Equations

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

Table of Contents:

• Graphing Linear Equations
• Solved Examples
• FAQs

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″>

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

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