STANDARD FORM OF A LINEAR EQUATION Day 1

STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5. 5 a

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

If we move “ ” to the other side of the equation, we have ____________. linear This is still a ____ equation, but it is written in a different form. A linear equation in the form ________ standard form where A, B, and C are is in _______, integers.

A linear equation in the form ________ standard form where A, B, and C are is in _______, integers. 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 $2. 00 # adult tickets $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 $10. 00 # other CDs $15. 00

Example 2: Tell whether the equations below are in standard form. A NO B YES C NO D NO E YES F NO x-term + y-term = constant No fractions, no decimals ! 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. B.

C. D.

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

x-intercept is at y-intercept is at x intercept, We know that y = 0 at the ____ y to find the _____ x intercept. so we can plug in 0 for ___ We know that x = 0 at the ____ y intercept, x to find the _____ y intercept. so we can plug in 0 for ___

Example 4: Find the x & y intercepts of the following equations. A. Plug in 0 for y x- intercept Plug in 0 for x y-intercept

Example 4: Find the x & y intercepts of the following equations. B. Plug in 0 for y x- intercept Plug in 0 for x y-intercept

Example 4: Find the x & y intercepts of the following equations. C. Plug in 0 for y x- intercept Plug in 0 for x y-intercept

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

x- intercept y-intercept

Slope = y - intercept = x - intercept =

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.