91Ó°ÊÓ

Graphing a linear function involves plotting a straight line on a coordinate plane.
These functions are characterized by their constant slope and y-intercept.
The general form of a linear function is expressed as:

• \( y = mx + b \)

where:

• \( m \) represents the slope.
• \( b \) represents the y-intercept.

To graph a linear function:
You'll need to plot at least two points and draw a line through them.
These steps are quite straightforward, making linear equations one of the simplest forms to work with in algebra.
By determining the slope and y-intercept, you can fully outline how the graph will look and behave on any Cartesian plane.

The slope-intercept form is a way of writing linear equations so that they are easy to graph.
This form of a linear equation is particularly helpful because it gives you immediate information about the line.
The equation is expressed as:

• \( y = mx + b \)

where:

• \( m \) is the slope of the line.
• \( b \) is the y-intercept.

This format allows you to quickly identify how steep the line is and where it crosses the y-axis.

Understanding Slope

The slope, \( m \), tells you how fast or slow the line rises or falls.
For example, a slope of \( \frac{1}{3} \) means the line goes up 1 unit for every 3 units it goes right.
A positive slope indicates an upward trend from left to right, while a negative slope shows a downward trend.

Plotting points involves placing them on a graph according to their coordinates.
To graph linear equations effectively, begin by plotting the y-intercept.
For the function \( h(x) = \frac{1}{3}x + 2 \), the y-intercept is 2, corresponding to the point \( (0, 2) \).

Using the Slope

After placing the y-intercept, use the slope to find another point.
If the slope is \( \frac{1}{3} \), you move 3 units horizontally to the right and 1 unit up.
This gives you the point \( (3, 3) \).
With these two points, you can draw a straight line through them.
Extend this line in both directions to show the linear function as it continues on the plane.
By understanding how to plot points using the slope-intercept form, you'll find graphing linear functions simple and intuitive.