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6-4 Standard Form

6-4 Standard Form. You will be learning 3 different forms (or formats) for writing linear equations. Slope-intercept form Standard form Point-slope form. Standard Form A x + B y = C. A, B, & C are real numbers. Ex. 2 x + 3 y = 6. A can be zero Ex. 5 y = 10

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6-4 Standard Form

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  1. 6-4 Standard Form

  2. You will be learning 3 different forms (or formats) for writing linear equations. • Slope-intercept form • Standard form • Point-slope form

  3. Standard Form Ax + By = C A, B, & C are real numbers. Ex. 2x + 3y = 6 A can be zero Ex. 5y = 10 B can be zero Ex. 6x = 12 C can be zero Ex. 6x + 5y = 0 A and B cannot BOTH be zero. If they were, your equation would be 0 = C…doesn’t make sense!

  4. When an equation is written in standard form, you can calculate the x-intercept and the y-intercept. The x-intercept tells where the line passes through the x-axis. The value of “y” at this point is zero. To find the value of “x” at this point, just set “y” equal to zero. Ex. 4x + 2y = 8 If I set y=0, I will find the x-intercept. 4x + 2(0) = 8 4x = 8 x = 2 So the x-intercept is 2

  5. When an equation is written in standard form, you can identify the x-intercept and the y-intercept. The y-intercept tells where the lines passes through the y-axis. The value of “x” at this point is zero. To find the value of “y” at this point, just set “x” equal to zero. Ex. 4x + 2y = 8 If I set x=0, I will find the y-intercept. 4(0)+ 2y = 8 2y = 8 y= 4 So the y-intercept is 4

  6. Ex. 4x + 2y = 8 Set x = 0 4(0)+ 2y = 8 2y = 8 y= 4 y-intercept is 4 set y=0 4x + 2(0) = 8 4x = 8 x = 2 x-intercept is 2 I can graph the line based on these two points.

  7. Some word problems are easiest to solve using the standard form. Example: Your school is sponsoring a ziti dinner to raise money for a field trip that costs $4000. You estimate the 200 adults and 250 children will attend. How much should the ticket prices be? Let x be the adult price and y be the kid price. You know that you want to raise a total of $4000. We know how many adults & kids (& the variables for prices). If we add the adult & kid info, we can get the total. # of adults * cost per adult + # of kids * cost per kids = total income 200x + 250y = 4000 So now you’re wondering… How does this help me?

  8. Let’s graph our equation 200x + 250y = 4000 Set x = 0 250y = 4000 y = 16 The y-intercept is 16 set y=0 200x = 4000 x = 20 The x-intercept is 20 Ziti Dinner x is the price for adults and y is the price for kids… If I charge $16 per kid and $0 per adult, I will reach my goal! If I charge $20 per adult and $0 per kid, I will also reach my goal. The line formed by connecting the points represents ALL other possible price combinations that will allow me to reach my goal! Kid Price Adult Price

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