Finding the slope-intercept form of a linear equation ($y = mx + b$) from two given points involves a few key steps. First, calculate the slope ($m$) using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Then, use one of the given points and the calculated slope to solve for the y-intercept ($b$) by substituting the values into the slope-intercept equation and solving for $b$. Finally, write the equation in the form $y = mx + b$ using the values you found for $m$ and $b$.
Let's solidify this with a worksheet!
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 form of linear equation: $y = mx + b$. |
| 3. Slope-intercept form | C. The measure of the steepness and direction of a line. |
| 4. Point | D. A location in a coordinate plane, represented by (x, y). |
| 5. Linear Equation | E. An algebraic equation in which each term is either a constant or the product of a constant and (in the case of one variable) a single variable. |
Match the correct pairs:
To find the slope-intercept form from two points, first calculate the _____. Then, use one of the points and the _____ to solve for the _____. Finally, write the equation in the form $y = mx + b$.
Possible Answers:
Explain why knowing the slope and y-intercept is useful for graphing a linear equation.
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