SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

§6.1 Rate of Change and Slope

deion avatar
deion
14 diapositives · 384 Views · Jul 30, 2014

§6.1 Rate of Change and Slope. Warm-Up. Evaluate each function rule for x = –5. 1. y = x – 7 2. y = 7 – x 3. y = 2 x + 5 4. y = – x + 3 Write in simplest form. 5. 6. 7. 2 5. 7 – 3 3 – 1. 3 – 5 6 – 0. 8 – (–4) 3 – 7. Warm-Up (Solutions).

#§6.1 rate of change and slope #§6.1 rate of change and slope ppt #powerpoint #presentation
§6.1 Rate of Change and Slope - slide 1
01 / 14§6.1 Rate of Change and Slope
1 / 17

Télécharger la présentation

§6.1 Rate of Change and Slope
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. §6.1 Rate of Change and Slope

  2. Warm-Up Evaluate each function rule for x = –5. 1. y = x – 7 2.y = 7 – x 3.y = 2x + 5 4.y = – x + 3 Write in simplest form. 5.6.7. 2 5 7 – 3 3 – 1 3 – 5 6 – 0 8 – (–4) 3 – 7

  3. Warm-Up (Solutions) 1.y = x – 7 for x = –5: y = –5 – 7 = –12 2.y = 7 – x for x = –5: y = 7 – (–5) = 12 3.y = 2x + 5 for x = –5: y = 2(–5) + 5 = –10 + 5 = –5 4.y = – x + 3 for x = –5: y = – (–5) + 3 = 2 + 3 = 5 5. = = 2 6. = – = – 7. = – = –3 2 5 2 5 7 – 3 3 – 1 4 2 3 – 5 6 – 0 2 6 1 3 8 – (–4) 3 – 7 12 4

  4. Vocabulary Rate of Change: the relationship between two quantities that are changing. The rate of change is also called the slope. change in the dependent variable rate of change = change in the independent variable Slope: the ratio of the vertical change to the horizontal change. vertical changey2 – y1 slope = = , where x2 – x1 does not = 0. horizontal change x2 – x1

  5. For the data in the table, is the rate of change the same for each pair of consecutive mileage amounts? Fee for Miles Driven Miles Fee 100 $30 150 $42 200 $54 250 $66 Example 1: Finding Rate of ChangeUsing a Table Find the rate of change for each pair of consecutive mileage amounts.

  6. change in costCost depends on the change in number of milesnumber of miles. rate of change = Fee for Miles Driven 42 – 301254 – 421266 – 5412 150–100 50 200–150 50 200–250 50 = = = Miles Fee 100 $30 150 $42 200 $54 250 $66 Example 1: Finding Rate of ChangeUsing a Table (continued) The rate of change for each pair of consecutive mileage amounts is $12 per 50 miles. The rate of change is the same for all the data.

  7. Below is a graph of the distance traveled by a motorcycle from its starting point. Find the rate of change. Explain what this rate of change means. Choose two points On the graph (0,0) and (20,400) Example 2: Finding Rate of ChangeUsing a Graph

  8. vertical changechange in distance horizontalchangechange in time rate of change = 400 – 0 20 – 0 400 20 20 Use two points. = Divide the vertical change by the horizontal change. = Simplify. = Example 2: Finding Rate of ChangeUsing a Graph (continued) Using the points (0,0) and (20,400), find the rate of change. The rate of change is 20 m/s. The motorcycle is traveling 20 meters each second.

  9. a. rise run 4 – 1 0 – 2 slope = = 3 –2 3 2 = = – 3 2 The slope of the line is – . Example ¥: Finding SlopeUsing a Graph Find the slope of each line.

  10. Find the slope of the line. b. rise run 1 – -1 -1 – (-2) slope = = 2 1 = = 2 Example ¥: Finding SlopeUsing a Graph (continued) The slope of the line is 2.

  11. –1 – (–2) –2 – 3 = y2 – y1 x2 – x1 slope = Substitute (–2, –1) for (x2, y2) and (3, –2) for (x1, y1). Simplify. 1 –5 1 5 = = – 1 5 The slope of EF is – . Example 3: Finding SlopeUsing Points Find the slope of the line through E(3, –2) and F(–2, –1).

  12. a. y2–y1 x2 – x1 slope = 2 – 2 1– (–4) Substitute (1, 2) for (x2, y2) and (–4, 2) for (x1, y1). Simplify. = 0 5 = = 0 Example 4: Finding Slope ofHorizontal and Vertical Lines Find the slope of the line. The slope of all horizontal lines is 0.

  13. y2 – y1 x2 – x1 slope = Substitute (2, 1) for (x2, y2) and (2, –4) for (x1, y1). 1 – (–4) 2 – 2 = 5 0 = Simplify. Example 4: Finding Slope ofHorizontal and Vertical Lines (continued) Find the slope of the line. b. Division by zero is undefined. The slope of all vertical lines is undefined.

  14. Assignment: Pg. 298-299 8-37 Left OMIT 27, 29, 31, 35