📚 Topic Summary
Writing linear equations from a slope and a point involves using the point-slope form, which is a handy tool to construct the equation of a line. The point-slope form is expressed as $y - y_1 = m(x - x_1)$, where $m$ represents the slope of the line, and $(x_1, y_1)$ is the given point on the line. By substituting the given slope and the coordinates of the point into this formula, you can easily derive the equation of the line. After substitution, simplify the equation into slope-intercept form ($y = mx + b$) if needed for further analysis or graphing purposes.
🧮 Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Slope |
A. A form of linear equation: $y = mx + b$ |
| 2. Point-Slope Form |
B. The 'b' value in slope-intercept form |
| 3. Y-intercept |
C. A form of linear equation: $y - y_1 = m(x - x_1)$ |
| 4. Slope-Intercept Form |
D. The measure of the steepness of a line |
| 5. Linear Equation |
E. An equation that, when graphed, forms a straight line. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided:
(Slope, Point-Slope, Equation, Coordinates, Intercept)
To write a linear __________ from a __________ and a point, use the __________ form. Substitute the __________ of the given point and the __________ into the formula to find the linear equation. The final result is the _________ of the line.
🤔 Part C: Critical Thinking
Explain in your own words why the point-slope form is useful for finding the equation of a line when you know a point on the line and its slope.