Chapter 4 Notes

Graphing Linear Equations and Functions

4.1 Coordinates and Scatter Plots

Objectives:-Plot points in a coordinate plane-Draw scatter plots and make predictions about the data

Terms

Coordinate Plane

Ordered pair

X-coordinate

Y-coordinate

Labeling the Coordinate plane

Plotting PointsPlot the following

points

a.(0,3)

b.(-2, -1)

c. (2,0)

d.(4,5)

Locating Quadrants

Find the quadrant of the following points (0,3) (-2, -1) (2,0) (4,5)

Making a Scatter Plot

4.2 Graphing Linear Equations Part1

Objectives:

-Make a list of values for a given equation

Terms

Solution of an Equation

Function Form

Function Form

Rewrite the equations in function form (y=mx+b)

-3x + y = 12

2x + 3y = 6

Function Form

Rewrite the equations in function form (y=mx+b)

-x – y = 5

5x + 5y = 20

T-Charts

Rules for t-ChartsEquations must be in function formChoose numbers for xSubstitute them in for xSolve for yRepeat to get a total of 3 values for your

function

T-Charts

Make a table of values(T-Chart) for each function

Y = -2x – 6 y = 3(6x – 1)

X Y YX

T-Charts

Make a table of values(T-Chart) for each function

Y = 3x - 5 y = 7 – 4x

X Y YX

Special Cases

When the equation has an X but no Y

Ex: x = 5

When the equation has a y but no x

Ex: y = 8

4.2 Graphing Linear Equations Part2

Objectives:

-Graph linear equations and make t- charts

T-Charts

Rules for t-ChartsEquations must be in function formChoose numbers for xSubstitute them in for xSolve for yGraph the values

Graphing

Y = 4x – 2 y = 2(x – 1)X Y YX

Graphing

2x + 2y = 10 5x – 7 = 5yX Y YX

4.3 Quick Graphs Using Intercepts

Objectives:-Find the x and y intercepts-graph a linear equation using the x and y intercepts

Terms

X- intercept

Y- intercept

Finding the x-intercept

X-intercepts always have ordered pairs in the form (#,0)

To find the x-intercept you plug 0 in for y and solve for x.

Finding the y-intercept

y-intercepts always have ordered pairs in the form (0,#)

To find the y-intercept you plug 0 in for x and solve for y.

Practice

Given the x and y intercepts graph the equation x-intercept = 2; x-intercept = -4;

y-intercepts = -3 y-intercepts = 5

Finding x and y -intercept

5x + 4y = -20

6x – y = 6

Finding x and y -intercept

-3x + y = -6

3x – y = -2

4.4 Slope

Objectives:

-Find the slope of a line given 2 pts

Terms

Slope

Rate of change

Finding Slope form a Graph

A

B

Finding Slope with a Formula

my y

x x

2 1

2 1

Slope = change in y

change in x

Special cases

#/0 means slope = undefined (U)

0/# means slope = 0

Practice

(2,3)(4,-5)

(1,-5)(-5,2)

(3,6)(3,0)

(0,5)(7,5)

Practice

(4,1)(6,-3)

(2,2)(-3,5)

(-6,-1)(-6,-4)

(0,-10)(-4,0)

White Board Practice

One person from each row get white boards and accessories

4.6 Quick Graphs Using Slope Intercept

Objectives:

-Graph a linear equation in slope intercept form

Terms

Slope-intercept form

Parallel lines

Perpendicular Lines

Locating slope and intercept

Given an equation in y=mx+b form

m=slope (pattern) b= y-intercept (start pt.)

Slope must be a fraction !!!

How it works

1st you start on the y axis at the b value

2nd you use your slope to rise and run from the b value

Practice

Graph each of the following and tell the slope and intercept

Y = 2x – 3

Y= -3x – 2

Y= ½ x + 5

Practice

Graph each of the following and tell the slope and intercept

Y= 2/3x – 1

Y= 2x

2y + 3x = 6