6-2 Slope-Intercept Form
What is Slope-Intercept Form?
Slope-Intercept Form is a way of expressing linear equations in the form of y = mx + b, where m is the slope and b is the y-intercept. This form is useful for graphing linear equations and identifying the slope and y-intercept of a line.
6-2 Slope-Intercept Form
In the 6-2 Slope-Intercept Form, we will learn how to write an equation in slope-intercept form, given the slope and y-intercept. We will also learn how to graph a line using the slope and y-intercept.
Writing an Equation in Slope-Intercept Form
To write an equation in slope-intercept form, we need to know the slope (m) and the y-intercept (b). The equation will be in the form of y = mx + b.
For example, if the slope is 2 and the y-intercept is 3, the equation would be:
y = 2x + 3
Graphing a Line Using Slope-Intercept Form
To graph a line using slope-intercept form, we need to know the slope (m) and the y-intercept (b).
- Start by plotting the y-intercept (b) on the y-axis.
- Use the slope (m) to find another point on the line. For example, if the slope is 2, move 2 units up and 1 unit to the right from the y-intercept.
- Draw a line through the two points to graph the line.
Example
Suppose we have a line with a slope of 3 and a y-intercept of 2. We can write the equation in slope-intercept form as:
y = 3x + 2
To graph the line, we start by plotting the y-intercept (2) on the y-axis. Then, we use the slope (3) to find another point on the line. For example, we can move 3 units up and 1 unit to the right from the y-intercept, which gives us the point (1, 5). Finally, we draw a line through the two points to graph the line.
Key Concepts
- Slope-Intercept Form: y = mx + b
- Slope (m): a measure of how steep a line is
- Y-Intercept (b): the point where the line crosses the y-axis
- Graphing a line using slope-intercept form involves plotting the y-intercept and using the slope to find another point on the line.
Practice Exercises
- Write an equation in slope-intercept form for a line with a slope of 4 and a y-intercept of 1.
- Graph a line with a slope of 2 and a y-intercept of 3.
- Identify the slope and y-intercept of a line with the equation y = x + 2.
