Slope Intercept Form Worksheet With Answers
Slope-intercept form is a way of expressing the equation of a line in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form is useful for graphing lines and finding the equation of a line given the slope and y-intercept.
What is Slope-Intercept Form?
The slope-intercept form of a linear equation is y = mx + b, where:
- m is the slope of the line, which represents the rate of change of the line.
- b is the y-intercept, which is the point where the line crosses the y-axis.
How to Graph a Line in Slope-Intercept Form
To graph a line in slope-intercept form, follow these steps:
- Plot the y-intercept (b) on the y-axis.
- Use the slope (m) to find another point on the line.
- Draw a line through the two points.
Examples of Slope-Intercept Form
Example 1: Find the equation of the line with a slope of 2 and a y-intercept of 3.
Using the slope-intercept form, the equation of the line is y = 2x + 3.
Example 2: Graph the line with the equation y = -x - 2.
Using the slope-intercept form, the y-intercept is -2, so plot the point (0, -2) on the y-axis. The slope is -1, so the line will decrease by 1 unit for every 1 unit increase in x.
Practice Problems
Find the equation of the line in slope-intercept form for each of the following problems:
| Problem | Slope (m) | y-Intercept (b) | Equation |
|---|---|---|---|
| 1 | 3 | 2 | y = 3x + 2 |
| 2 | -2 | 1 | y = -2x + 1 |
| 3 | 1/2 | -3 | y = (1/2)x - 3 |
| 4 | -3 | 0 | y = -3x |
| 5 | 2/3 | 1 | y = (2/3)x + 1 |
Answers
1. y = 3x + 2
2. y = -2x + 1
3. y = (1/2)x - 3
4. y = -3x
5. y = (2/3)x + 1
📝 Note: The slope-intercept form is a useful way to express the equation of a line, and it can be used to graph lines and find the equation of a line given the slope and y-intercept.
By practicing with these problems, you can become more comfortable using the slope-intercept form to find the equation of a line and graph it on a coordinate plane.
To summarize, the slope-intercept form is a way of expressing the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept. By using this form, you can easily graph lines and find the equation of a line given the slope and y-intercept.
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 and b is the y-intercept.
How do I graph a line in slope-intercept form?
+To graph a line in slope-intercept form, plot the y-intercept (b) on the y-axis, use the slope (m) to find another point on the line, and draw a line through the two points.
What is the equation of the line with a slope of 2 and a y-intercept of 3?
+The equation of the line is y = 2x + 3.
