Linear Relations

Linear Relations Formula: a mathematical statement that shows a relationship between specific quantities. Ex. A = πr2 Area of a circle radius r

Example 1: Graph from a Linear Formula   Sound travels 1500 m/s in salt water. This relationship can be express by the formula d = 1500t, where d is the distance travelled, in meters, and t is the time, in seconds. a) Make a table of Values and then Graph the values. d 8000 7000 6000 5000 4000 3000 2000 1000 t d 1 1500 2 3000 3 4500 4 6000 5 7500 6 9000 7 10500 d = 1500(t) d = 1500(1) d = 1500 1st letter (answer of the formula) goes to the 2nd column Distance (m) 0 1 2 3 4 5 6 7 8 9 t b) Is it reasonable to have points between the ones on this graph?    Yes c) Calculate the distance sound travels in 3.5 seconds? d = 1500t d = 1500 (3.5) d = 5250 m Sound travels 5220 meters in 3.5 seconds. Time (s)

a) Make a table of Values and then Graph the values. Example 2 - James rents a lawnmower for $8 per hour. A formula representing this relationship is C = 8t, where C is the rental cost, in dollars, and t is the time, in hours.  a) Make a table of Values and then Graph the values. d 64 56 48 40 32 24 16 8 t C 1 8 2 16 3 24 4 32 5 40 6 48 C = 8(t) c = 8 (0) c = 8 Cost ($) b) Is it reasonable to have points between the ones on this graph? Maybe, but can you really rent it for half an hour? c) Calculate the cost to rent for 12 hours? C = 8t C = 8(12) C = 96 Cost to rent the lawnmower is $96 0 1 2 3 4 5 6 7 8 9 t Time( h)

y Example 3 – Graph from a Linear Equation Using Integers Use the linear equation y = -3x + 4 to complete the flowing steps.  a) Make a table of Values and then Graph the values. x y -2 10 -1 7 4 +1 1 +2 y = -3x + 4 y = -3(-2) + 4 y = 6 + 4 y = 10 coordinate (point on graph or table) x b) Determine the value for y in the order pair (11, y). y = -3x + 4 = -3(11) + 4 = -33 + 4 = -29 y = -3x + 4

Look off the table of values or off the graph (0,3) y-axis Example 4 – Graph from a Linear Equation Using Integers Use the linear equation y = 2x + 3 to complete the flowing steps.  a) Make a table of Values and then Graph the values. y = -2x + 3 x y -2 -1 1 3 +1 5 +2 7 y = 2x + 3 y = 2(-2) + 3 y = -4 + 3 y = -1 x-axis b) What are the coordinates for the point that would lie on the y-axis? Look off the table of values or off the graph (0,3) Algebraically use formula y = 2x +3 x = 0 y = 2(0) + 3

9.3 Linear Relation