The point-slope form is a way to express the equation of a line using a single point on the line and the slope of the line. It's especially handy when you know a point and the slope, but not the y-intercept. The formula is: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.
Using the point-slope form, you can easily write the equation of a line and then manipulate it into other forms, like slope-intercept form ($y = mx + b$). Understanding this form gives you a powerful tool for solving various problems related to linear equations. Let's test your knowledge!
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Slope | A. The point where the line crosses the y-axis. |
| 2. Point-Slope Form | B. A measure of the steepness of a line. |
| 3. Y-intercept | C. The ratio of the vertical change to the horizontal change between two points on a line. |
| 4. Linear Equation | D. $y - y_1 = m(x - x_1)$ |
| 5. Coordinate Pair | E. An equation that forms a straight line when graphed. |
Complete the following paragraph using the words provided (slope, point, equation, line, form):
The point-slope ______ is a useful way to write the ______ of a ______. You need a ______ on the line and the ______ to use this form.
Explain how you can use the point-slope form to find the slope-intercept form of a line. Give an example.
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