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STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a
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The equation is written _______________ form. If we move “ we have _______________________. ” to the other side of the equation, slope intercept
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If we move “ we have _______________________. ” to the other side of the equation, This is still a ________ equation, but it is written in a different form. linear A linear equation in the form _______________ is in ______________, where A, B, and C are integers. standard form
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A linear equation in the form _______________ is in ______________, where A, B, and C are integers. standard form Remember the set of integers is. NO FRACTIONS!!! NO DECIMALS !!!
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Example 1: A.Jackie is in charge of selling tickets for the school jazz concert at $2.00 for students and $4.00 for adults. She hopes that the total ticket sales will be about $600 in order to cover expenses and make a modest profit. Write a linear equation in standard form to model this situation. Let # student tickets # adult tickets $2.00 $4.00
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B.A donation of $300 was make to the Classical Music Club for the purpose of building their collection of CDs. At the local music store, some classical CDs cost $10 and other cost $15. The club wants to know how many of each type can buy with the $300. (Do not consider sales tax.) Write an equation in standard form to model this situation. Let # classical CDs # other CDs $10.00 $15.00
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x-term + y-term = constant No fractions, no decimals ! A B C D E F Example 2: Tell whether the equations below are in standard form. NO YES NO YES NO FRACTIONS DECIMALS
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If an equation is not written in standard form, we can rewrite the equation so that it is in standard form. Example 3: Write each linear equation in standard form. A.A. B.B.
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C.C. D.D.
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We can find the ___& ___ intercepts and the ________ when the equation is written in standard form. xyslope x-intercept is at y-intercept is at
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x-intercept is at y-intercept is at We know that y = 0 at the ____ intercept, so we can plug in 0 for ___ to find the _____ intercept. We know that x = 0 at the ____ intercept, so we can plug in 0 for ___ to find the _____ intercept. x yx y yx
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Example 4: Find the x & y intercepts of the following equations. A.A. x- intercept y-intercept Plug in 0 for y Plug in 0 for x
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Example 4: Find the x & y intercepts of the following equations. B.B. x- intercept y-intercept Plug in 0 for y Plug in 0 for x
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Example 4: Find the x & y intercepts of the following equations. C.C. x- intercept y-intercept Plug in 0 for y Plug in 0 for x
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x- intercept y-intercept Write in slope-intercept form to find the slope.
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x- intercept y-intercept
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x - intercept = y - intercept = Slope =
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x - intercept = y - intercept = Slope = To find the x-intercept, cross out the y-term…
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x - intercept = y - intercept = Slope = To find the y-intercept, cross out the x-term…
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Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept
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Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept
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If an equation is written in standard form, you can use the _______________ to graph the equation quickly. x & y intercepts
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Example 6: Graph the following equations. A.
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Example 6: Graph the following equations. A.
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Example 6: Graph the following equations. A.
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Example 6: Graph the following equations. B.
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Example 6: Graph the following equations. B.
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Example 6: Graph the following equations. B.
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Example 6: Graph the following equations. C.
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Example 6: Graph the following equations. C.
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Example 6: Graph the following equations. C.
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Example 6: Graph the following equations. D.
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Example 6: Graph the following equations. D.
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Example 6: Graph the following equations. D.
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