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Try reviewing these fundamentals first.

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Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

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Let's put the linear functions in words! It's not hard to find things with linear relations around us. We will show you how to solve linear relationship word problems.

Basic concepts: Representing patterns in linear relations, Reading linear relation graphs, Solving linear equations by graphing,

- 1.The value $V$ of a classic toy car, in dollars, is given by $V + 15t = 350$, where $t$ is the age of the car. If the car was bought new 5 years ago, graph the equation and estimate the value of the car 6 years from now.
- 2.The cost $C$, in dollars, of renting a hall for the prom is given by the formula $C(n) = 500 + 4n$, where $n$ is the number of students attending the prom. Calculate the cost of renting the hall if 70 students attend.
- 3.Sam completes a puzzle in time $t$ (mins) is related to number of tries ($n$). The resulting equation is $t = 30 - {4 \over 5}n$ Graph the equation and estimate the time it takes him to do the puzzle on his $15^{th}$ try.
- 4.A game rental store charges $15.00 to rent the console and the game and $3.00 per additional hour. Write the linear equation. Determine the cost of renting for 15 hours. Determine the hours if the cost was $150.
- 5.In 1970 the population of Andyland city was 900,000, in 1995 the population of the same city had grown to 1,500,000.

i) Find the average rate of change for the population of this city from 1970 to 1995.

ii) Predict how many people will live in this city in 2015. - 6.A car repair shop charges an hourly rate plus a fixed amount. One hour costs $70, and four hours costs $160.

i) Determine the hourly rate.

ii) Write the equation that shows the total cost ($C$) in terms of number of hours ($H$) and the fixed cost ($F$).

iii) Domain and Range. - 7.Jack has two options when renting his car for the vacation:

Option A: $50 per day, and no extra charge per kilometre.

Option B: $35 per day, and 15 cents per kilometre.

i) Graph the options $A$ & $B$

ii) How many kilometres must Jack travel to make option $A$ the cheapest rate?

8.

Linear Functions

8.1

Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

8.2

Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

8.3

Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$

8.4

Gradient intercept form: y = mx + b

8.5

General form: Ax + By + C = 0

8.6

Gradient-point form: $y - y_1 = m (x - x_1)$

8.7

Rate of change

8.8

Graphing linear functions using table of values

8.9

Graphing linear functions using x- and y-intercepts

8.10

Graphing from slope-intercept form y=mx+b

8.11

Graphing linear functions using a single point and gradient

8.12

Word problems of graphing linear functions

8.13

Parallel and perpendicular lines in linear functions

8.14

Applications of linear relations

8.15

Perpendicular line equation

We have over 1420 practice questions in AU Essential Maths for you to master.

Get Started Now8.1

Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

8.2

Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

8.3

Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$

8.4

Gradient intercept form: y = mx + b

8.5

General form: Ax + By + C = 0

8.6

Gradient-point form: $y - y_1 = m (x - x_1)$

8.7

Rate of change

8.12

Word problems of graphing linear functions

8.13

Parallel and perpendicular lines in linear functions

8.14

Applications of linear relations

8.15

Perpendicular line equation