Linear Graphs Linear Applications Lesson Objective To understand

Linear Graphs Linear Applications

Lesson Objective To understand how linear graphs are used in everyday life Lesson Success Criteria • Can identify when a linear graph is present between variables in everyday life • Can interpret the y-intercept, and gradient in the context of the problem

Practical applications of linear graphs In everyday life there are many occasions where relationships between variables can be modelled with a linear (or straight-line) graph. • • Income vs hours worked Distance travelled vs time travelled Costs of hiring a van vs number of hours hired Dollars vs number of cell-phone minutes used

Interpreting in Context What does the y-intercept mean? • Represents the value of y initially (i. e. when x=0) • Could represent a fixed fee, initial charge, callout fee etc. What does the gradient represent? • Represents the rate at which y changes compared to x • Could represent a hourly pay rate, or hourly hire charge etc

Example George the plumber quotes his customers the following, “I charge a call out fee of $50, and $60/hr on top” Question: 1. Form an equation to represent his charges 2. What does the y-intercept mean in context? 3. What does the gradient mean in context? 4. Using a suitable scale plot on a graph 5. For a job that takes 2 hours, how much would it cost me? 6. How much work would I get for $350?

Example

More than 1 equation George the plumber quotes his customers the following, “I charge a call out fee of $50, and $60/hr on top” Percy the plumber quotes his customers the following, “I charge my customers $75 an hour, but only $20 call out” Which plumber would you call for your plumbing needs and why?

Example

More than 1 equation From the graph: There is an intersection point at h = 2, i. e. for jobs that are 2 hours, both plumbers charge the same amount, which is $170. For jobs less than 2 hours, I would hire Percy, as his charges are less than George. This is shown by the Percy’s line being lower than George. For jobs greater than 2 hours, I would hire George, as his charges are less than Percy. Shown by his line being lower than Percy’s.

More than 2 equations Quite possibly you would have 3 or even 4 different people, suppliers, lines to compare. Your objective is to compare all three,

Homework Exercise I, pg. 91: Applications of linear graphs