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# Formulas

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### Formulas

1. 1. Lesson 1-3 Formulas
2. 2. The Coordinate Plane <ul><li>In the coordinate plane, the horizontal number line (called the x- axis) and the vertical number line (called the y- axis) interest at their zero points called the Origin. </li></ul>Definition: x - axis y - axis Origin
3. 3. The Distance Formula <ul><li>Find the distance between (-3, 2) and (4, 1) </li></ul>x 1 = -3, x 2 = 4, y 1 = 2 , y 2 = 1 The distance d between any two points with coordinates and is given by the formula d = . Example: d = d = d =
4. 4. Midpoint Formula Find the midpoint between (-2, 5) and (6, 4) x 1 = -2, x 2 = 6, y 1 = 5, and y 2 = 4 Example: In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and are . M = M =
5. 5. Slope Formula Find the slope between (-2, -1) and (4, 5). Example: Definition: In a coordinate plane, the slope of a line is the ratio of its vertical rise over its horizontal run. Formula: The slope m of a line containing two points with coordinates and is given by the formula where .
6. 6. Describing Lines <ul><li>Lines that have a positive slope rise from left to right. </li></ul><ul><li>Lines that have a negative slope fall from left to right. </li></ul><ul><li>Lines that have no slope (the slope is undefined) are vertical. </li></ul><ul><li>Lines that have a slope equal to zero are horizontal. </li></ul>
7. 7. Some More Examples <ul><li>Find the slope between (4, -5) and (3, -5) and describe it. </li></ul>Since the slope is zero, the line must be horizontal. <ul><li>Find the slope between (3,4) and (3,-2) and describe the line. </li></ul>Since the slope is undefined, the line must be vertical. m = m =
8. 8. Example 3 : Find the slope of the line through the given points and describe the line. <ul><li>(7, 6) and (– 4, 6) </li></ul>Solution: This line is horizontal. x y (7, 6) up 0 left 11 (-11) (– 4, 6) m
9. 9. Example 4: Find the slope of the line through the given points and describe the line. <ul><li>(– 3, – 2) and (– 3, 8) </li></ul>Solution: This line is vertical. x y (– 3, – 2) up 10 right 0 (– 3, 8) undefined m
10. 10. Practice <ul><li>Find the distance between (3, 2) and (-1, 6). </li></ul><ul><li>Find the midpoint between (7, -2) and (-4, 8). </li></ul><ul><li>Find the slope between (-3, -1) and (5, 8) and describe the line. </li></ul><ul><li>Find the slope between (4, 7) and (-4, 5) and describe the line. </li></ul><ul><li>Find the slope between (6, 5) and (-3, 5) and describe the line. </li></ul>