Mini Quiz Find the domain and range of the function: 2. What is the greatest value in the range of y=2x+4 for the domain {-2, -1, 0, 1}

Quick Preview The diagram at the right shows the side view of a ski lift. What is the vertical change from: A to B? B to C? C to D? What is the horizontal change from: C to D 10 feet 40 feet 30 feet Find the ratio of the vertical change to the horizontal change for each section of the ski lift. Which section is the steepest? A 1 B 4 C 1 B 3 C 3 D 3 = ; = ; = B to C

6-1 Slope Objective: 1. To find rates of change from tables and graphs 2. To find slope

What is the rate of change for the data to the left? Rate of Change-a ratio that describes, on average, how much one quantity changes with respect to a change in another quantity. If x is the independent variable and y is the dependent variable, then: What is the rate of change for the data to the left? change of dependent = $15 change of independent = 1 day $15 = $15/day 1 day What does the rate of change mean? It cost $15 more to rent a computer each day.

Slope Think, pair, share: What do you know about slope? Where might you see slope? What might we use slope for?

Slope Slope is the slant of a line slope = m = rise run Always write as an improper fraction in simplest form rise = up (+) down (-) run = right (+) left (-)

How steep is the steepest roller coaster? Ghost Rider Knott’s Berry Farm The Magnum Cedar Point, OH Superman 6 Flags Magic Mountain Xcelerator Knott’s Berry Farm These are completely vertical! Son of Beast King’s Island, OH How steep is the steepest roller coaster?

Positive slope writes up, negative slope writes down Generalizations Can we make any generalizations? You can start at either point negative positive + − Positive slope writes up, negative slope writes down

Undefined Zero slope special cases = 0 How do these lines look different? Vertical and horizontal 5. rise = 0 run = 2 2. rise = 4 run = 0 Undefined Zero slope Error – can’t divide by 0!! Undefined = no slope = 0

Pick two points on the line Calculate “rise over run” How do you calculate the slope of a line? There are 3 steps: Pick two points on the line Calculate “rise over run” Determine the sign

Start with 2 points on gridline intersections Step 1 Start with 2 points on gridline intersections (2, 3) OK OK Not OK OK (1, 1) Not OK OK (0, -1) Not OK OK (-1, -3)

Slope Directions: Find the slope given two points. (x1,y1) (x2, y2) m = y2 − y1 x2 − x1 m = slope Plug the numbers into the formula!

Examples Find the slope given two points. (3,10) (12,5) m = 5 − 10 12 − 3 (-1,5) (-3,7) m = 7 – 5 -3 – (-1) -3 + 1 x1 y1 x2 y2 x1 y1 x2 y2 = -5 9 = 2 -2 = -1

Undefined (-2,3) (-2,-3) m = -3 – 3 -2 – (-2) Zero on bottom of fraction #/0 Vertical line Same x’s in ordered pairs x1 y1 x2 y2 = -3 - 3 -2 + 2 = -6 = Undefined

Zero Slope (-1,4) (2,4) m = 4 – 4 2 – (-1) Zero on top of fraction 0/# horizontal line Same y’s in ordered pairs x1 y1 x2 y2 = 4 - 4 2 + 1 = 0 3 = Zero slope

Tell a partner How do you find the slope given a line? How do you find the slope given two points? What does a positive/negative slope look like?

Before you leave: 1. What type of slope is shown? (Positive, negative, zero or undefined?) 2. What would a slope of -1/2 look like? (Uphill, downhill, steep, shallow) 3. What is the slope of the line above?