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Warm Up for 9.6

Warm Up for 9.6. Find the distance and midpointbetween the following sets of points. (5, 19) and (-3, -1) (7, -16) and (-2, -1) (1, -4) and (0, 0) (-6, 4) and (5, 20). Answers: distance. Answers: midpoint (1,9) (5/2, -15/2) (-1/2, -2) (-1/2, 12). Slope: algebra review #4.

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Warm Up for 9.6

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  1. Warm Up for 9.6 Find the distance and midpointbetween the following sets of points. • (5, 19) and (-3, -1) • (7, -16) and (-2, -1) • (1, -4) and (0, 0) • (-6, 4) and (5, 20) Answers: distance • Answers: midpoint • (1,9) • (5/2, -15/2) • (-1/2, -2) • (-1/2, 12)

  2. Slope:algebra review #4 What is slope? What is the slope formula? Slope = The steepness of a line.

  3. Example 1 and 2: Find the slope between the two points. a. ( 7,6) and (3,1) Plug the numbers into the slope formula andsimplify b. ( -3, -15) and ( -5, 1) Plug the numbers into the slope formula andsimplify Watch out for DOUBLE NEGATIVES!

  4. Last two examples: Example 3: find the slope of (7, 8) and (7, 5) undefined Plot the points and connect. “SLICES” through the x-axis at 7 • You can not have zero in the denominator so if you do the answer is “undefined” x=7 • The graph of a line with a undefined slope will be a vertical line. x y

  5. Example 4: Find the slope of (5,9) and (-3,9) Plot the points and connect. “SLICES” through the y-axis at 9 • When zero is in the numerator the answer is just zero. y=9 x • The graph of a line with zero slope is a horizontal line y

  6. Parallel and Perpendicular Lines • Lines that are parallel have _____________________________. • Lines that are perpendicular have ____________________________. the same slope opposite reciprocal slopes This means opposite signs and the fractions are flipped.

  7. Discovering Parallel Lines • Predict which of the following will be parallel. • y = ½x + 1 • y = -3x – 4 • y = ½x – 4 • y = -½x + 1 1 and 2 since the slopes are the same.

  8. Discovering Perpendicular Lines • Predict which lines will be perpendicular, explain your reasoning. • y = 4x + 1 • y = -4x + 1 • y = ¼x – 3 • y = x – 1 2 and 3 since one slope is negative, the other is positive and they are reciprocals of each other.

  9. WRAP UP Find the slope and perpendicular slopes between the following sets of points. • (5, 19) and (-3, -1) • (7, -16) and (-2, -1) • (1, -4) and (0, 0) • (-6, 4) and (5, 20) Answers: The parallel slopes are the same. The perpendicular slopes are…. Negative Reciprocals! Opposite sign and flip!!!

  10. Summary: • EXPLAIN WHAT IS THE SLOPE OF A LINE: FORMULA, HORIZONTAL LINE, VERTICAL LINE • EXPLAIN HOW TO FIND THE SLOPE OF ANOTHER LINE THAT IS PARALLEL TO AN EXISTING LINE. • EXPLAIN HOW TO FIND THE SLOPE OF ANOTHER LINE THAT IS PERPENDICULAR TO AN EXISTING LINE. Homework: Slope review worksheet

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