Graphing Lines by points Section 4.2 GRAB SOME GRAPH PAPER #26 I used to love mathematics for its own sake, and I still do, because it allows for no hypocrisy and no vagueness.... ~Stendhal (Henri Beyle), The Life of Henri Brulard 1-10, odd, odd, 42-47

Uses of ordered pairs Apart 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

Graphing solutions When 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 equations For 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 equations For example: Our previous example yields some solutions, but not all of them Y X In order to show all of the solutions we draw a line through the points

Rules for Lines as Solutions There are a set of rules that we have to follow when drawing lines as solutions 1. Lines have to go through three points in order to establish consistency 2. Arrowheads are used to show the infinite number of solutions

Write this DOWN Steps for Plotting Points 1. Draw axes 1.Use a Straightedge 2.Label X, Y 3.Include arrowheads 2. Determine a Scale 1.Label several points 3. Find and Plot 3 points 1.Write coordinate pair next to point 4. Draw line 1.Use a Straightedge 2.Connect all three points 3.Draw Arrowheads

Practice Y X xy=x+5

You try Y X xy=4x-1

Standard Form Linear 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 Form In order to put an equation into the format that we’re used to working with, we simply solve for y Y X

Y X X & Y Intercepts We 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 Lines H O Y V U X Horizontal Horizontal Horizontal Horizontal zero zero Slope Slope zero zero Slope Slope Y Y Y Equals Equals Y Y Equals Equals Vertical Vertical Vertical Vertical undefined undefined undefined undefined X X X Equals Equals X X Equals Equals

Horizontal & Vertical Lines But that doesn’t follow the standard form for lines y=a x=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

Solve for Y and graph  Rewrite the following equations to solve for y  4x+2y=16

Solve for Y and graph  Rewrite the following equations to solve for y  -6x-3y=-12

Practice Y X y Y=-2x+3

Most Important Points  Plotting with points  Using practical examples to show relationships between independent (x) and dependent (y) variable

Homework , odd, 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

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.