Chapter 6: Linear Function Group Member: Angela, Vincent, Krystal, Antony.

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Presentation transcript:

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

Slope Slope 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.

Example Calculate 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 Lines If two lines have the same slope, the two lines parallel to each other. Example: y=2x+1 and y=2x+3

Perpendicular Lines If 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 : 2 So, the slope of the line should be: 2 So, 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 : 2 So, the slope of the line should be: -1/2 So, 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 AD Step 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 Form y-intercept form: y=2x+1 Advantage: We can easily determine the intersection with y-axis

Slope-Point Form Slope-point form: y-y 1 =m(x 1 -x 2 ) Example: y-2=1/3*(x+4) Advantage: We can easily know that (-4,2) is on this line.

General Form General form can be represented as: ax+by+c=0 Example: 2x+3y-12=0 Hint: You should always check the order-----x y number