Linear Equations: Exploring Independent and Dependent Variables The equation y = x + 10 is a linear equation, where x is the independent variable and the y is the dependent variable. The value of the y depends on the value of the x.

Caleb is x years old. His sister is 10 years older that Caleb Caleb is x years old. His sister is 10 years older that Caleb. If the sister is y years old, write an equation “representing the value of y in terms of x.” Caleb Sister x x +10 y y = x + 10

Caleb is x years old. His sister is 10 years older that Caleb Caleb is x years old. His sister is 10 years older that Caleb. If the sister is y years old, write an equation “representing the value of y in terms of x. A table of values can be used to organize the relationship. Caleb’s Age (x) y = x + 10 Sister’s Age (y) 2 y = 2 + 10 12 3 y = 3 + 10 13 4 y = 4 + 10 14 10 y = 10 + 10 20

Charlie earns d dollars for doing his house chores per week Charlie earns d dollars for doing his house chores per week. Sam earns half of what Charlie earns per week. If g is the amount Sam earns, write an equation expressing g in terms of d. Charlie Sam d ½ d g g = ½ d or g = d/2

Charlie earns d dollars for doing his house chores per week Charlie earns d dollars for doing his house chores per week. Sam earns half of what Charlie earns per week. If g is the amount Sam earns, write an equation expressing g in terms of d. A table of values can be used to organize the relationship. Charlie Earns (d) g = ½ d Sam Earns (s) 10 g = ½ (10) 5 30 g = ½ (30) 15 80 g = ½ (80) 40 100 g = ½ (100) 50

Tables to Ordered Pairs to Coordinate Planes Let’s take a closer look at our first table. USING THIS LINEAR EQUATION, WE CAN DETERMINE THE VALUE OF THE SISTER’S AGE (DEPENDENT). AS A RESULT, WE HAVE AN ORDERED PAIR THAT CAN BE GRAPHED ON A COORDINATE PLANE. Caleb’s Age (x) y = x + 10 Sister’s Age (y) 2 y = 2 + 10 12 3 y = 3 + 10 13 4 y = 4 + 10 14 10 y = 10 + 10 20 (2,12) (3,13) (4,14) (10,20) Continued… (next slide)

SISTER’S AGE CALEB’S AGE COMPARING CALEB’S AGE TO HIS SISTER’S AGE 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 11 (2,12) (3,13) (4,14) (5,15) (6,16) 12 13 14 15 16 17 1 1 1 1 1 1 1 IF THE TREND CONTINUED, HOW OLD WOULD CALEB’S SISTER BE WHEN HE TURNS 24 YEARS OLD? HOW OLD WOULD CALEB BE WHEN HIS SISTER TURNS 50?

Creating equations from situations… Identifying the independent and dependent variables. Situation #1 – (low complexity) George is g years old. His sister, Kim, is 8 years older than George. If Kim is k years old, create an equation representing Kim’s age (k) in terms of g.

Situation #2 – (medium complexity) Creating equations from situations… Identifying the independent and dependent variables. Situation #2 – (medium complexity) Emma is shopping for school supplies. She bought a binder for $4 and some felt tip pens at $1.20 each. Let c represent the total cost of her purchase and f represent the number of felt tip pens. Write an equation that models the situation.

Situation #3 – (higher complexity) Creating equations from situations… Identifying the independent and dependent variables. Situation #3 – (higher complexity) Each ride at the carnival costs $2. If you spend $5 on cotton candy and $3 on a drink, determine the total amount you spent at the carnival if you went on x rides. Let c represent the total cost and write an equation modeling the situation.