Lesson Plan / Slope / Middle School grades

1. Slope Teacher: Mr. Valdivia Email – [email_address] Grade Level: 8 Subject: Mathematics NGSSS: MA.8.A.1.2 Interpret the slope…when graphing a linear equation for a real-world problem. Also MA.8.A.1.1

2. Opening Questions Have you ever been skiing? What is the difference between a beginner’s trail, often called the bunny slope, and the expert’s trail, often called the black diamond slope? Which one of the two would have a steeper slope? Can we calculate the slope of a trail? Click for video http://player.discoveryeducation.com/index.cfm?guidAssetId=086D0622-99B1-4997-BADE-0166B07F6625&blnFromSearch=1&productcode=US

3. Rise: The vertical change when the slope of a line is expressed as the ratio rise/run. Run: The horizontal change when the slope of a line is expressed as the ratio rise/run. Slope: A measure of steepness (or constant rate of change) of a line on a graph . Vocabulary Distancia Vertical: El cambio vertical cuando la pendiente de una linea se expresa como la razon distancia vertical/distancia horizontal Distancia Horizontal: El cambio horizontal cuando la pendiente de una linea se expresa como la razon distancia vertical/distancia horizontal. Pendiente: Medida de la inclinacion (o la tasa de cambio constante) de una linea en una grafica. Razon de la distancia vertical a la distancia horizontal. Vocabulario

4. The constant rate of change of a line is called the slope of the line. The rise is the difference of the y-values of two points on a line. The run is the difference in the x-values of two points on a line. The slope of a line is the ratio of rise to run for any two points on the line. Y is the dependent variable . X is the independent variable .

5. (5, 4) (1, 2) Then count horizontally to a second point to find the run. Count vertically from any one point on the line to find the rise. Finding the Slope of a Line slope = = 2 4 1 2 The slope of the line is . 1 2 – 2 – 4 slope = = 1 2

6. (3, 2) (–1, –2) Then count horizontally to a second point to find the run. Count vertically from any one point on the line to find the rise. Finding the Slope of a Line slope = = 1 4 4 The slope of the line is 1. – 4 – 4 slope = = 1

7. If you know any two points on a line, or two solutions of a linear equation, you can find the slope of the line without graphing. The slope m of a line through the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is as follows: y 2 – y 1 x 2 – x 1 m =

8. Find the slope of the line that passes through (–2, –3) and (4, 6). Finding Slope, Given Two Points Let ( x 1 , y 1 ) be (–2, –3) and ( x 2 , y 2 ) be (4, 6). Substitute 6 for y 2 , –3 for y 1 , 4 for x 2 , and –2 for x 1 . 6 – (–3) 4 – (–2) 9 6 = The slope of the line that passes through (–2, –3) and (4, 6) is . 3 2 = y 2 – y 1 x 2 – x 1 3 2 =

9. Find the slope of the line that passes through (–4, –6) and (2, 3). Finding Slope, Given Two Points Let ( x 1 , y 1 ) be (–4, –6) and ( x 2 , y 2 ) be (2, 3). Substitute 3 for y 2 , –6 for y 1 , 2 for x 2 , and –4 for x 1 . 3 – (–6) 2 – (–4) 9 6 = The slope of the line that passes through (–4, –6) and (2, 3) is . 3 2 = y 2 – y 1 x 2 – x 1 3 2 =

10. Example Problem The table shows the total cost of gas per gallon. Use the data to make a graph. Find the slope of the line and explain what it shows. Graph the data. Cost of Gas Gallons Cost 0 0 3 6 6 12 6 9 9 12 6 0 3 3 x y Gallons Cost of Gas Cost

11. Example Problem Continued Find the slope of the line: The slope of the line is 2. This means that for every gallon of gas, you will pay another $2. = y 2 – y 1 x 2 – x 1 6 3 = 12 – 6 6 – 3 = 2

12. The slope of a line my be positive, negative, zero, or undefined.

13. The slope of a line my be positive, negative, zero, or undefined.

14. Lesson Quiz: Part I 1. (4, 3) and (–1, 1) 2. (–1, 5) and (4, 2) Assessment Find the slope of the line passing through each pair of points. 2 5 5 3

15. Lesson Quiz: Part II 3. The table shows how much money Susan earned as a house painter for one afternoon. Use the data to make a graph. Find the slope of the line and explain what it shows. Assessment x y 6 4 2 8 10 12 14 0 10 20 30 40 50 60 70 80 The slope of the line is 7. This means Susan earned $7 for each hour worked.

16. 2. The table shows the number of hours a student works and her earnings. Identify the slope of the line and explain what it shows. A. The slope of the line is 15. This means that the student earns $15 for every hour that she works. B. The slope of the line is 30. This means that the student earns $30 for every hour that she works. Quiz Student Response