positive negative

gentle

steep

continuous

discrete

PreCalculus 10Chapter 6.1 Graphs of Relations

Basic Concepts and Terminology of Graphing:

Y-axis: Vertical axisDependent axis, meaning that the value of y depends on the value of x.

X-axis: Horizontal axisIndependent axis, (input or category axis)

Y depends on X

Linear Relation: y is proportional to x. As a result, the graph forms a straight line.

Slope of the Line: a) Positive – y increase if x increase; y decrease if x decreaseb) Negative – y decrease if x increase; y increase if x decrease

c) Steep – Rate of increase is biggerd) Gentle – Rate of increase is smaller

Discrete data: There are no in-between values. The “graph” will be represented by individual points

Continuous data: There are in-between values. The graph will form a line.

Chapter 6 – Linear Relations and Functions

24

22

20

18

16

14

12

10

8

6

4

2

0

Cost ($)

Number of toppings0 1 2 3 4 5 6

Cost of Take Out Pizza

PreCalculus 10Example:

The cost of a take-out pizza is a good example of linear relations of data. The cost (y-axis) depends on the number of toppings (x-axis) order. For example, a basic large pizza cost $10.00. Any additional topping cost $2.00. The relation can be expressed in two ways:

1) Table of Value:

2) Graphing:

The data forms a linear relation because the increase of the cost (y-axis) is directly proportional to the increase of the number of toppings (x-axis) - $2 for extra toppings. The data forms a straight line on the graph.

What is the equation to find the Cost (C) of pizza based on the number of toppings (n):

Chapter 6 – Linear Relations and Functions

Number of toppings (n) 0 1 2 3 4 5Cost (C) $10 $12 $14 $16 $18 $20

Positive sloperise

run

Negative slope rise

run

x

y

P2(x2, y2)

P1(x1, y1)

PreCalculus 106.5 Slope (p.315 – 324)

Linear relation – same slope through the line (straight line).

Non-linear relation – different slope at different point on the line.

The slope of a line is a measure of how steep the line is. The slope also describes the direction of the line.

The pitch of a roof, the steepness of a ski run, or the gradient of a mountain road are all examples of slope.

The letter is used to represent slope The slope is the ratio of the rise to the run

Find the slope of line segment with end points and

In general:

Chapter 6 – Linear Relations and Functions

RISE = Y2 – Y1

RUN = X2 – X1

Therefore:

Slope formula:

change in corresponding change in

y

x

A

B

C

D

PreCalculus 10Example:

Find the slope of the following lines:A) B)

C) D)

Sample problems:1) Determine the slope of the following line

segments:a) A(2, 1), B(6, 8) c) M(-5, 4), N(3, -1)

b) X(3, 5) and Y(3, -4) d) J(2, 4) and K(-5, 4)

Using Slope to graph a line

Sketch the graph of the line that passes through the given point and has the given slope,

a. (-2, -3), slope = 2/3

b. (-3, 4), slope = -4/3

c. (0, 2), slope = -1/2

d. (-1, 0), slope = 3/2

Homework:Textbook:P. 325, Q 1, 2, 3(a,c,e), 4, 5, 8, 14, 16

Chapter 6 – Linear Relations and Functions