PreCalculus 10

Chapter 6.1 Graphs of Relations

Basic Concepts and Terminology of Graphing:

Y-axis:Vertical axis

Dependent axis, meaning that the value of y depends on the value of x.

X-axis:Horizontal axis

Independent 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 decrease

b) Negative – y decrease if x increase; y increase if x decrease

c) Steep – Rate of increase is bigger

d) 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.

Example:

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:

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

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):
6.5 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:

Example:

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,

  1. (-2, -3), slope = 2/3
  1. (-3, 4), slope = -4/3
  1. (0, 2), slope = -1/2
  1. (-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