In mathematics, a linear equation represents a straight line on a graph. The slope-intercept form of a linear equation is a way to easily write these equations. This form is expressed as $y = mx + b$, where $m$ represents the slope of the line (the rate of change of $y$ with respect to $x$), and $b$ represents the y-intercept (the point where the line crosses the y-axis). Given the slope and y-intercept, you can directly substitute these values into the equation to define the line.
Understanding the slope-intercept form allows you to quickly create equations for lines. For example, if you know a line has a slope of 2 and crosses the y-axis at 3, the equation is simply $y = 2x + 3$. This worksheet will provide practice in applying this concept.
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Slope | A. The point where the line crosses the y-axis. |
| 2. Y-intercept | B. A symbol that represents a value that can change. |
| 3. Linear Equation | C. The rate of change of $y$ with respect to $x$. |
| 4. Variable | D. An equation that, when graphed, forms a straight line. |
| 5. Coordinate | E. A set of values that show an exact position. |
Complete the following paragraph using the words provided: slope, y-intercept, equation, line, point.
The slope-intercept form of a linear ________ is $y = mx + b$, where $m$ represents the ________ and $b$ represents the ________. The ________ $(x, y)$ lies on the ________.
Explain how changing the slope affects the graph of a linear equation. Provide an example.
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