STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a

The equation is written _______________ form. If we move “ we have _______________________. ” to the other side of the equation, slope intercept

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

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 !!!

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

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

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

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.

C.C. D.D.

We can find the ___& ___ intercepts and the ________ when the equation is written in standard form. xyslope x-intercept is at y-intercept is at

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

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

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

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

x- intercept y-intercept Write in slope-intercept form to find the slope.

x- intercept y-intercept

x - intercept = y - intercept = Slope =

x - intercept = y - intercept = Slope = To find the x-intercept, cross out the y-term…

x - intercept = y - intercept = Slope = To find the y-intercept, cross out the x-term…

Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. A.A. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. B.B. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept

Example 5: Find the slope and x & y intercepts of the following equations. C.C. A = B = C = Slope x- intercept y-intercept

If an equation is written in standard form, you can use the _______________ to graph the equation quickly. x & y intercepts

Example 6: Graph the following equations. A.

Example 6: Graph the following equations. A.

Example 6: Graph the following equations. A.

Example 6: Graph the following equations. B.

Example 6: Graph the following equations. B.

Example 6: Graph the following equations. B.

Example 6: Graph the following equations. C.

Example 6: Graph the following equations. C.

Example 6: Graph the following equations. C.

Example 6: Graph the following equations. D.

Example 6: Graph the following equations. D.

Example 6: Graph the following equations. D.