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LINEAR RELATIONSHIPS. This has to do with lines. Lines are formed from sets of points. Each point has an x-coordinate and a y-coordinate. The equation of a line tells us the connection between the x and y coordinates for each point. Consider the following diagram. (1,8). (3,6). (5,4).

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linear relationships
LINEAR RELATIONSHIPS

This has to do with lines.

Lines are formed from sets of points.

Each point has an x-coordinate and a y-coordinate.

The equation of a line tells us the connection between the x and y coordinates for each point.

Consider the following diagram.

slide2

(1,8)

(3,6)

(5,4)

(7,2)

(9,0)

For each of these points the “x-value + the y-value = 9”

So the equation of the line is x + y = 9

slide3

Now consider this diagram.

(8,6)

(6,4)

(4,2)

(2,0)

(0,-2)

For each of these points the “y-value = the x-value - 2”

So the equation of the line is y = x - 2

slide4

Example 1

Draw the line y = 2x – 1 .

To get the y-value we double the x-value then take away 1.

We can choose our own x-values

x -2 -1 0 1 2

y

-5

-3

-1

1

3

We can now draw a graph.

slide6

Example 2

Draw the line y = 1/3x + 2 .

To get the y-value we divide the x-value by 3 then add 2.

We can choose our own x-values

x -6 -3 0 3 6

y

0

1

2

3

4

We can now draw a graph.