Chapter 6: Linear Function

Group Member: Angela, Vincent, Krystal, Antony

What is slope? What is the formula to calculate slope? How to determine slope through two points on a line?

How to verify a parallel line or a perpendicular line to a given one?

How to calculate a parallel or a perpendicular line to a given one?

How to use slope to identify polygon?Three different forms of writing an equation of a linear

function.Using an Equation of a Linear Function to Solve a

Problem.

Agenda

SlopeSlope is the steepness of a roof is measured by calculating

its slope.The formula of the slope is: Slope= Rise/Run

Hint: Rise: The vertical distance from the bottom of edge of the roof to

the top Run: The corresponding horizontal distance.

ExampleCalculate the slope of

the linear function.

From the graph, we can see that the rise=2, the run=1. Then we can calculate the slope: Slope=Rise/Run =2/1 =1

Parallel LinesIf two lines have the same slope, the two lines parallel to

each other.Example: y=2x+1 and y=2x+3

Perpendicular LinesIf two line perpendicular to each other, that means that

the two slopes are negatively reciprocal to each other.

Example: y=2x+1 and y=-1/2 x+1

In this graph, the linear function of this line is y=2x+1. Can you write a linear function that is parallel to the line?

How to determine a parallel line to a given one?

Solution

The parallel line and the given line should have the same slope. The slope of the given line is : 2So, the slope of the line should be: 2So, the linear function of the line should be y=2x+2/3/4, etc.

In this graph, the linear function of this line is y=2x+1. Can you write a linear function that is perpendicular to the line?

How to determine a perpendicular line to a given one?

Solution

The perpendicular line’s slope the negative reciprocal of the slope of the given line.

The slope of the given line is : 2So, the slope of the line should be: -1/2So, the linear function of the line should be y=-1/2x + 1/2/3/4, etc.

ABCD is a parallelogram. Is it a rectangle? Justify the answer.

How to use slope to identify polygon?

a

b

c

d

Solution

ABCD is a parallelogram. If one of the angle is 90, we can prove that it is a rectangular.

Step 1: we can determine the slope of line AB and line ADStep 2: we can identify whether the slope of AB is the negative reciprocal

of slope AD.Step 3:we can easily identify whether it is a rectangle or not.

Slope-Intercept Formy-intercept form: y=2x+1Advantage: We can easily determine the intersection with y-axis

Slope-Point FormSlope-point form: y-y1=m(x1-x2)

Example: y-2=1/3*(x+4)

Advantage: We can easily know that (-4,2) is on this line.

General FormGeneral form can be represented as: ax+by+c=0

Example: 2x+3y-12=0

Hint: You should always check the order-----x y number