How to Graph a Linear Function: Step-by-Step Guide with Examples

Linear Function Graph

A linear function graph is a representation of a linear equation using a straight line

A linear function graph is a representation of a linear equation using a straight line. It shows the relationship between the independent variable (usually represented as x) and the dependent variable (usually represented as y). The general form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

To graph a linear function, you need to plot two points on the coordinate plane and draw a straight line that passes through these points. Here’s how you can do it:

1. Identify the slope (m) and the y-intercept (b) from the given linear equation. The slope determines the steepness of the line, while the y-intercept is the point where the line intersects the y-axis.

2. Start by plotting the y-intercept on the y-axis. The y-intercept is the point (0, b).

3. Next, use the slope to find another point. The slope represents the change in y divided by the change in x. For example, if the slope is 2/3, it means that for every increase of 3 units in x, y increases by 2 units. Use this information to find a second point on the line.

4. Plot the second point on the graph.

5. Draw a straight line passing through the two points you plotted. Make sure the line extends beyond the points in both directions.

6. Label the x-axis and y-axis with appropriate values.

Remember, the slope can be positive, negative, zero, or undefined, which will impact the direction of the line on the graph. Here are a few examples to illustrate:

Example 1:
Let’s say the linear equation is y = 2x + 3.
– The slope (m) is 2.
– The y-intercept (b) is 3.
Plot the point (0, 3) and find another point using the slope, such as (1, 5). Connect these points with a straight line.

Example 2:
For a vertical line equation, x = 4.
– There is no slope (undefined).
– The line crosses the x-axis at x = 4.
Draw a vertical line passing through (4, 0).

Example 3:
For a horizontal line equation, y = -2.
– The slope is 0.
– The line crosses the y-axis at y = -2.
Draw a horizontal line passing through (0, -2).

It’s important to remember that linear functions are represented by straight lines, and their graphs follow consistent patterns based on the slope and y-intercept.

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