Linear Function and graphs

Content

Example 1

Let say you get a magical box that works as follows.

If you put 1 sweet in the box, it returns 2 sweets.

If you put 2 sweets in the box, it returns 4 sweets.

If you put x sweets in the box, it returns y sweets.

y = 2(x) = 2x sweets.

Example 2

1 cup of Coffee costs $ 0.80

2 cups of Coffee costs = 2 x 0.80 = $ 1.60

m cups of Coffee costs $c

c = m(0.80) = 0.8m

c = 0.8m

Example 3

A Mobile Phone service provider charges as follows.

Fixed Charge : $10/month

Outgoing Call rates : $0.10/minute

If you do not make any calls at all in a month, you just pay the Fixed Charge $10 for that month

If you make Outgoing calls for 5 minutes in a month, you pay 0.10(50) + 10 = 5 + 10 = $15 for that month

If you make Outgoing calls for k minutes in a month, your payment will be $Y

y = 0.10 k + 10

Two variables x and y has a linear relationship if y can be expressed as y = mx + c, where m and c are constants.

Draw the lines : y = 6 – 2x and y = 4x – 6

To draw a straight line, find co-ordinates (x,y) of 3 points.

Mark the co-ordinates in graph paper and connect them with straight lines

Equation of this line is y = 2x, so the gradient is 2.

Vertical Shift = 4 – 2 = 2.

Horizontal shift = 2 – 1 = 1.

Gradient = Vertical shift / horizontal shift = 2/1 = 2.