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- Linear Functions

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!

Get Started Now- Lesson: 12:28
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Rate of change is all around us. For example, we express the speed of a car as Kilometer per hour (km/hr), the wage in a fast food restaurant as dollar per hour, and taxi fare as dollar per meter or kilometer. Let's solve some word problems on rate of change.

Basic concepts: Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$, Slope intercept form: y = mx + b, Point-slope form: $y - y_1 = m (x - x_1)$,

Related concepts: Representing patterns in linear relations, Applications of linear equations, Graphing linear inequalities in two variables, Graphing systems of linear inequalities,

Rate of change = ${{{\bigtriangleup y} \over {\bigtriangleup x} } = { {y_2 -y_1} \over {x_2 -x_1}}}$Examples: km/hr, miles per gallon, m/s, dollars/hr, etc.

- 1.Draw a graph to describe the fare charged by a taxi with an initial cost of $10.50 plus $2.50 per km traveled.
- 2.Draw a graph to describe the income of a insurance sales person who earns $800 per month plus $400 for every car sold.
- 3.A long distance runner passes the 36 km mark of a race in 1 hr 40 mins, and passes the 44 km mark 1 hr 10 mins later. If the rate is constant, find the speed of the long distance runner in km/hr.
- 4.Cathy hires a super band to play at a wedding. The cost for the wedding was $1000 for the band, plus $50 per guest for food and $3 per guest for beverages. Determine the cost per person if 150 guests attended the wedding, and averaged three drinks per person.

3.

Linear Functions

3.1

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

3.2

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

3.3

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

3.4

Gradient intercept form: y = mx + b

3.5

General form: Ax + By + C = 0

3.6

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

3.7

Rate of change

3.8

Graphing linear functions using table of values

3.9

Graphing linear functions using x- and y-intercepts

3.10

Graphing from gradient-intercept form y=mx+b

3.11

Graphing linear functions using a single point and gradient

3.12

Word problems of graphing linear functions

3.13

Parallel and perpendicular lines in linear functions

3.14

Applications of linear relations

We have over 1230 practice questions in NZ Year 12 Maths for you to master.

Get Started Now3.1

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

3.2

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

3.3

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

3.4

Gradient intercept form: y = mx + b

3.5

General form: Ax + By + C = 0

3.6

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

3.7

Rate of change

3.12

Word problems of graphing linear functions

3.13

Parallel and perpendicular lines in linear functions

3.14

Applications of linear relations