Bellwork Write the coordinates for the following points

Over 4 to the right from the origin and up 3 from the x-axis Down 4 from the origin and left 3 from the y-axis Left 1 from the origin and down 7 from the x-axis

Rewrite the following equations to solve for y 4x+2y=16 -6x-3y=-12

No Clickers

Bellwork Solution Write the coordinates for the following points

Over 4 to the right from the origin and up 3 from the x-axis

Down 4 from the origin and left 3 from the y-axis

Left 1 from the origin and down 7 from the x-axis

X=4 Y=3 (4, 3)

Y=-4 X=-3 (-3, -4)

X=-1 Y=-7 (-1, -7)

Bellwork Solution Rewrite the following equations to solve for y

4x+2y=16

82216

24

22

16421624

xy

xyxy

yx

Bellwork Solution Rewrite the following equations to solve for y

-6x-3y=-12

42312

36

33

12631236

xy

xyxy

yx

Graphing Lines by pointsSection 4.2

Uses of ordered pairsApart from being used exclusively as a graphing tool,

ordered pairs also yield us solutions to equations

For Example: A solution to the equation 3x-y=7 can be what? Any number of sets of ordered pairs Typically we’re given one number of the ordered pair x=3 y=2

x Solution-2 2(-2)+1= -3 (-2,-3)-1 2(-1)+1= -1 (-1,-1)0 2(0)+1= 1 (0,1)1 2(1)+1= 3 (1,3)2 2(2)+1= 5 (2,5)

y=2x+1

Graphing solutionsWhen we use a T-table to denote

points in which to graph, we are creating a table of solutions to our equations

For Example:

Solutions to equationsFor most equations, there are infinite number of solutions

to each linear equation.Each line includes all points that serve as these solutions

because a solid line is the nomenclature for inclusion of points

Solutions to equationsFor example: Our previous example yields some solutions, but

not all of them

x Solution-2 2(-2)+1= -3 (-2,-3)-1 2(-1)+1= -1 (-1,-1)0 2(0)+1= 1 (0,1)1 2(1)+1= 3 (1,3)2 2(2)+1= 5 (2,5)

y=2x+1

Y

XIn order to show all of the solutions we draw a line through the points

Rules for Lines as SolutionsThere are a set of rules that we have to follow when

drawing lines as solutions1. Lines have to go through three points in order to

establish consistency2. Arrowheads are used to show the infinite number of

solutions

Steps for Plotting Points1. Draw axes

1. Use a Straightedge2. Label X, Y3. Include arrowheads

2. Determine a Scale1. Label several points

3. Find and Plot 3 points1. Write coordinate pair next to point

4. Draw line1. Use a Straightedge2. Connect all three points3. Draw Arrowheads

PracticeY

X

x y=x+5

Standard FormLinear equations follow many formats Standard Form is the one that appears as:

We use this form because it’s our most standard understanding of linear equations

ax+by=c

Still our x-coordinate Still our

y-coordinate

Standard FormIn order to put an equation into

the format that we’re used to working with, we simply solve for y

53210

26

)610(21

61021062

xy

xy

xy

xyxy

Y

X

X & Y InterceptsWe can get a lot of information from a graph A useful piece of information is the x-intercept and the

y-intercept X-intercept is where the line crosses the x-axis or where y=0 Y-intercept is where the line crosses the y-axis or where x=0

x intercept

y intercept

Horizontal & Vertical LinesHorizontal and Vertical Lines have the following equations

y=a

x=a

Horizontal & Vertical LinesBut that doesn’t follow the standard form for lines

y=ax=a

No matter what the x, y is always going to equal a No matter what

the y, x is always going to equal a

Homework

4.21-10, 11-21 odd, 23-39 odd, 42-47

Practical Example Example 5, Page 218 The distance d (in miles) that a runner travels is given by

the function d=6t where t is the time (in hours) spent running. The runner plans to go for a 1.5 hour run. Graph the function and identify it’s domain and range

PracticeY

X

t d=

Practical Example A fashion designer orders fabric that costs $30 per yard.

The designer wants the fabric to be dyed, which costs $100. The total cost C (in dollars) of the fabric is given by the function below, where f is the number of yards of fabric.

The designer orders 3 yards of fabric. How much does the fabric cost?

Suppose the designer can spend $500 on fabric. How many yards can the designer buy? Explain why.

30 100C f

Most Important Points Plotting with points Using practical examples to show relationships between

independent (x) and dependent (y) variable

PracticeY

X

x y=3x-1