Figure 1: Warm-Up 1 3 2 4 (1,1) (2,2) 5 (-1,-1) (4,2) 6 (-1,1) (2,4) Find the slope of the line segment represented by the graph (problems 1-3) or pair of points (problems 4-6) 1 2 3 Y Y Y 4 4 4 -4 4 X -4 4 X -4 4 X -4 -4 -4 4 (1,1) (2,2) 5 (-1,-1) (4,2) 6 (-1,1) (2,4) 7. Explain the difference between positive and negative slope

Figure 2: Problem Statement Lines on a graph can be expressed in the form y = m(x) + b + “Run” Y + “Rise” X The two feature which can define the graph of a line are: 1. Slope: 2. Y- Axis Intercept: (y value when x=0) “Rise” “Run” How are the terms “m” and “b” related to Slope and Y-Axis intercept?

Figure 3: Example Problems Y Graph the following lines using the calculator: 4 1. y= 2x+1 2. y=-2x+1 -4 4 X 3. y=-0.5x-1 4. y=0.5x-1 -4

Figure 4: Pair Exercise Questions 1-4: Graph each equation, and write equation (y=mx+b format) for each line Questions 5-7: Provide short answer Use Calculators to solve problems 1a, 1c, 2a, and 2c only. (May use calculators to check all answers) 1 b 2 4 Y Y b 4 d a y = x + 2 d a y = -x - 1 b b c y = x - 1 c y = 2x - 1 -4 4 X -4 4 X d d -4 -4 4 3 a Y Y a 4 b a 4 b y = (-3/4)x c a X=-2 c c b d y = (-1/4)x c y = 2 -4 4 X e -4 4 X e d d f y = (1/2)x g g -4 -4 h y = x 5. In equation y=mx+b, “m” represents_______________ 6. “b” represents___________________ 7. Without graphing the equation Y=2x-7, write everything you know about its graph (use back side) Note: Red dashed lines represent where students will draw lines

Figure 4a: Individual Practice Exercises Questions 1-4: Graph each equation, and write equation (y=mx+b format) for each line Use Calculators to check answers only 1 b 2 4 Y 4 Y a d a b b a y = -2x + 3 b y = -2x – 3 -4 4 X -4 4 X -4 -4 4 3 Y Y a 4 b a 4 c a a X=3 b b y = -3 -4 4 X -4 4 X d b -4 -4 5. In equation y=mx+b, “m” represents_______________ 6. “b” represents___________________ Note: Red dashed lines represent where students will draw lines

Figure 5: Word Problem y Start End 5,000 ft End 2,000 ft 10,000 ft A straight ski trail (see picture above) starts at 5,000 ft elevation above sea level. If the end of the trail is at 2,000 ft elevation above sea level, and 10,000 ft away (laterally): a. What is the average slope of the ski trail? b. What would be an equation that could relate elevation above sea level (y) to distance laterally from the start of the run (x)? (Hint: Determine starting point relative to origin first)

Figure 6: Homework Graph the following equations on Figure a: Y 1. y= 3x-3 4 2. y=-1/3x-3 3. y= 3x+3 -4 4 X 4. y=-1/3x+3 Write the equation of the lines in Figure b -4 5. y= Figure b 6. y= 5 7 Y 4 7. y= 8 6 8. y= 9. Word Problem -4 4 X From the word problem in class, find the elevation above sea level of the ski trail 1000 ft from the start. -4

Figure 7: Quiz Graph the following equations on Figure a: 1. y= 4x-4 Write the equation of the lines in Figure b -4 5. y= Figure b Y 6. y= 4 7. y= 5 7 Concept Explanation: -4 4 X 8. What do the ‘m’ and the ‘b’ represent in the equation: y=mx+b? 6 -4