Graphing Linear Equations (Slope-Intercept Form)
In this lesson, we will learn how to graph linear equations using the slope-intercept form. The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept. This method allows us to quickly plot the graph of a line by identifying these two key features.
Outline
- Introduction to Slope-Intercept Form
- Understanding Slope and Y-Intercept
- Examples of Graphing Linear Equations
- Exercises with Solutions
- Homework
- Revision Section
- Contact Us for Tutoring
Slope-Intercept Form
The slope-intercept form of a linear equation is y = mx + b. Here:
- m is the slope of the line, which represents how steep the line is.
- b is the y-intercept, which is the point where the line crosses the y-axis.
To graph a line using this form:
- Plot the y-intercept (0, b) on the y-axis.
- Use the slope m to determine the direction and steepness of the line. The slope is the ratio of the change in y to the change in x.
- Draw the line through the y-intercept with the given slope.
Examples of Graphing Linear Equations
Example 1:
Graph the equation y = 2x + 3. Here, the slope m = 2 and the y-intercept b = 3.
Example 2:
Graph the equation y = -x - 1. Here, the slope m = -1 and the y-intercept b = -1.
Example 3:
Graph the equation y = \frac{1}{2}x + 4. Here, the slope m = \frac{1}{2} and the y-intercept b = 4.
Example 4:
Graph the equation y = -2x + 2. Here, the slope m = -2 and the y-intercept b = 2.
Example 5:
Graph the equation y = 0.5x - 3. Here, the slope m = 0.5 and the y-intercept b = -3.
Example 6:
Graph the equation y = -3x + 5. Here, the slope m = -3 and the y-intercept b = 5.
Exercises
Exercise 1:
Graph the equation y = 3x - 2.
Exercise 2:
Graph the equation y = -\frac{1}{3}x + 1.
Exercise 3:
Graph the equation y = 4x + 3.
Exercise 4:
Graph the equation y = -2x - 5.
Exercise 5:
Graph the equation y = \frac{2}{5}x + 4.
Exercise 6:
Graph the equation y = -x + 6.
Solutions
Solution 1:
For y = 3x - 2: Plot the y-intercept (0, -2) and use the slope 3 to determine the direction.
Solution 2:
For y = -\frac{1}{3}x + 1: Plot the y-intercept (0, 1) and use the slope -\frac{1}{3} to determine the direction.
Solution 3:
For y = 4x + 3: Plot the y-intercept (0, 3) and use the slope 4 to determine the direction.
Solution 4:
For y = -2x - 5: Plot the y-intercept (0, -5) and use the slope -2 to determine the direction.
Solution 5:
For y = \frac{2}{5}x + 4: Plot the y-intercept (0, 4) and use the slope \frac{2}{5} to determine the direction.
Solution 6:
For y = -x + 6: Plot the y-intercept (0, 6) and use the slope -1 to determine the direction.
Homework
- Graph the following equations: y = 2x + 3, y = -x + 4, y = \frac{3}{4}x - 2.
- Label the y-intercept and use the slope to draw each line.
- Write a brief description of how the slope affects the graph of the line.
Revision
Review the following concepts:
- The slope-intercept form y = mx + b and its components.
- How to plot the y-intercept and use the slope to graph a line.
- Understanding how changes in slope and y-intercept affect the graph of the equation.
Watch the Video Tutorial
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