BackLinear Equations: Slope-Intercept Form and Graphing
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Linear Equations and Their Graphs
Slope-Intercept Form of a Linear Equation
The slope-intercept form of a linear equation is a standard way to express the equation of a straight line. It is especially useful for quickly identifying the slope and y-intercept of the line.
General Form:
Where:
m is the slope of the line (the rate of change of y with respect to x)
b is the y-intercept (the value of y when x = 0)
Example: Rewrite in slope-intercept form.
Start by isolating y:
Identifying Slope and Y-Intercept
Once the equation is in slope-intercept form, the values of the slope and y-intercept can be read directly.
Slope (m): The coefficient of x. In , the slope is 4.
Y-Intercept (b): The constant term. In , the y-intercept is -2.
Interpretation: For every increase of 1 in x, y increases by 4. The line crosses the y-axis at (0, -2).
Graphing a Linear Function Using Slope and Y-Intercept
To graph a line given its slope and y-intercept:
Plot the y-intercept: Start at the point (0, b) on the y-axis. For , plot (0, -2).
Use the slope: From the y-intercept, use the slope to find another point. A slope of 4 means "rise 4, run 1":
From (0, -2), move up 4 units and right 1 unit to (1, 2).
Draw the line: Connect the points with a straight line extending in both directions.
Example: Graph by plotting (0, -2) and (1, 2), then drawing the line through these points.
Summary Table: Slope-Intercept Form Components
Component | Description | Example Value |
|---|---|---|
Slope (m) | Rate of change; rise over run | 4 |
Y-Intercept (b) | Point where the line crosses the y-axis | -2 |
Equation | Slope-intercept form |
Additional info: The process of converting a linear equation to slope-intercept form is fundamental in precalculus and algebra, as it allows for easy graphing and interpretation of linear relationships.
