1. FINDING THE EQUATION OF A LINE 1.KNOWING A POINT AND THE SLOPE 2.KNOWING TWO POINTS

2. 1. KNOWING A POINT AND THE SLOPE The equation of the line through the point (x 1, y 1 ) with slope m is y = m x + b As y 1 = m x 1 + b we can find the value of b. Example: (x 1, y 1 ) = (2, 3) m = -1 y = - x + b 3 = -2 + b b = 5 Equation: y = - x + 5

3. 2. KNOWING TWO POINTS What is the equation of the line through (x 1, y 1 ) and (x 2, y 2 )? Find m=(y 2 – y 1 )/(x 2 – x 1 ) Do the same as before. Example: Line through (-1, 3) and (1, 6): m = (6 – 3)/(1 – (–1)) = 3/2 y = 1.5 x + b 6 = 1.5 + b; b = 4.5 y = 1.5 x + 4.5

4. PROBLEM I visited New York last year and the temperature was 95 degrees Fahrenheit. Did I need a T-shirt or a scarf? What was the equivalent temperature in degrees Celsius? The freezing point of water is 32 degrees Fahrenheit (°F) and the boiling point 212 °F (at standard atmospheric pressure).

5. CLUE 1 What is the freezing point of water in degrees Celsius? What is the boiling point of water in degrees Celsius? Which variable is x and which variable is y?

6. CLUE 2 x = “degrees Fahrenheit” y = “degrees Celsius” xy 320 212100 95??

7. CLUE 3 Is the relation between x and y linear? Can you find the equation of the line through (32, 0) and (212, 100)? When you know the equation you can find y = f(95)

8. EQUATION AND GRAPH

9. MORE QUESTIONS 1.Can you change the temperature right now to degrees Fahrenheit? 2.Look for the formulas to change temperatures in internet and compare your answers. 3.Who was Fahrenheit and why did he invent this scale of temperature? 4.Are there any other scales of temperature? 5.If the relationship between two variables is not linear, can we use the same method?