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Bellwork

Bellwork. No Clickers. 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

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Bellwork

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  1. Bellwork No Clickers • 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

  2. 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)

  3. Bellwork Solution • Rewrite the following equations to solve for y • 4x+2y=16

  4. Bellwork Solution • Rewrite the following equations to solve for y • -6x-3y=-12

  5. Graphing Lines by points Section 4.2

  6. 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

  7. 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:

  8. 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

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

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

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

  12. Y X Practice

  13. Still our x-coordinate Standard Form Still our y-coordinate 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

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

  15. 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 y intercept x intercept

  16. Horizontal & Vertical Lines Horizontal and Vertical Lines have the following equations y=a x=a

  17. 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

  18. Homework 4.2 1-10, 11-21 odd, 23-39 odd, 42-47

  19. 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

  20. Y X Practice

  21. 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 functionbelow, 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.

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

  23. Y X Practice

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