Equations of Lines

Equation of Lines Objectives: Discover the slope intercept form of the equation of a line. This graph shows the relationship between degrees Celcius and degees Fahrenheit. This is the graph of : 9 f  c  32 5 9 y  x  32 5 To convert from C to F, pick some degrees Celcius to convert: 9 f  c  32 5 Let’s say you want to convert 16°C to °F. Find 16°C on the x axis 9 f  c  32 5 Go straight up from 16° to the line. 9 f  c  32 5 16 °C = 61°F 9 f  c  32 5 From the line, go to the “f” axis. This is equal to 16°C in Fahrenheit! 16 °C = 61°F 16°C is equal to almost 61° Fahrenheit 9 f  c  32 5 You plug 16°C into the equation and see what you get. 9 f  c  32 5 9 (16) f   32 5 1 f  28.8  32 f  60.8 You will now be asked several questions about the graph of: 9 f  c  32 5 37 3°C= ___°F Plug 3°C into the equation and see what you get. 9 f  c  32 5 9 (3) f   32 5 1 f  5.4  32 f  37.4 48 9°C= ___°F 107.6 42°C= _____°F 5 42°F= _____°C 38 100°F= ____°C Complete the chart and calculate the slope of the line. x y -2 -4 -1 -1 0 2 1 5 2 8 Compare your calculated slope with the equation of the line. Do you see a relationship? 3 1 x -2 3x+2 -4 -1 -1 0 2 1 5 The Slope Formula •y2 - y1 x2 - x1 Compare your calculated slope with the equation of the line. Do you see a relationship? The slope is the 3 number in 1 front of the x -2 -1 1 0 “x”. 2 5 3x+2 -4 -1 When an equation is in slope-intercept form: Now look at the graph of each line. Look at where the graphs cross the “y” axis. What is the significance of this number in the equation? This is the yintercept (where the graph crosses the “y” axis). When an equation is in slope-intercept form: C-23 Slope-Intercept Conjecture: y=mx+b What is the equation of the line in slope-intercept form? 3 m = 4 b = -2 3 y  x2 4 What is the equation of the line in slope-intercept form? 2 m =  5 b =3 2 y   x3 5 What is the equation of the line in slope-intercept form? 1 m = 2 b = 4 1 y  x4 2 Graph the equation…. First calculate the slope and y-int. 2 y  x4 3 2 m = 3 b = -4 Plot the y-intercept. 2 y  x4 3 2 m = 3 b = -4 Apply slope from y-intercept. 2 y  x4 3 2 m = 3 b = -4 Draw line through two points. 2 y  x4 3 2 m = 3 b = -4 Graph each equation: 7 y  x 1 8 7 m = 8 b = 1 Graph each equation: y=-4x+6 m = -4 b = 6 True or False. The slope of 2 the line below is 5 . True or False. The yintercept of the line is -4. True or False. The equation of the line is: 2 y  x4 5