Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Eigenvalues and eigenvectors wikipedia , lookup
Linear algebra wikipedia , lookup
System of polynomial equations wikipedia , lookup
Signal-flow graph wikipedia , lookup
Cubic function wikipedia , lookup
Quartic function wikipedia , lookup
Quadratic equation wikipedia , lookup
Elementary algebra wikipedia , lookup
History of algebra wikipedia , lookup
STANDARD FORM OF A LINEAR EQUATION Students will be able to graph linear equations using intercepts and write linear equations in standard form. The equation y 2 x 3 is written _______________ form. slope intercept y 2 x 3 2x 2x y 3 If we move “ 2x ” to the other side of the equation, 2x y 3 we have _______________________. If we move “ 2x ” to the other side of the equation, 2x y 3 we have _______________________. linear This is still a ________ equation, but it is written in a different form. Ax By C A linear equation in the form _______________ standard form where A, B, and C are is in ______________, integers. Ax By C A linear equation in the form _______________ standard form where A, B, and C are is in ______________, integers. Remember the set of integers is ... 4, 3, 2, 1, 0, 1, 2, 3, 4... . NO FRACTIONS!!! NO DECIMALS !!! Tell whether the equations below are in standard form. A 5 y 2 4x NO 4 x 2 y 2 YES 5 y x8 7 2 x y 5 3 NO E 7 x 3 y 5 YES F 7.5x y 4.3 NO B C D 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. Write each linear equation in standard form. A. 57 2 y 4 x 2 y B. 7y 3 7x 8 7 7 57 4 x 2 y 4 x 2 y 57 7y 3x 56 3x 3 x 7 y 56 4 x 2 y 57 3 x 7 y 56 Convert this equation into standard form: Ax + By = C 2 y x 3 5 Multiply everything by 5 5y 2x 15 -2x Move over the “x” term -2x 2x 5y 15 2x 5y 15 IT CAN’T LEAD WITH A NEGATIVE!!! So let’s change the sign of each term. It’s kind of like moving backwards! Convert this equation into standard form: Ax + By = C y x 5 +x +x xy 5 Move over the “x” term Convert this equation into standard form: Ax + By = C 1 y x7 2 Multiply everything by 2 2y 1x 14 Move over the “x” term + 1x + 1x x 2y 14 Convert this equation into standard form: Ax + By = C 2 y x4 3 Multiply everything by 3 3y 2x 12 Move over the “x” term -2x -2x 2x 3y 12 2x 3y 12 IT CAN’T LEAD WITH A NEGATIVE!!! So let’s change the sign of each term. Write an equation of the line in STANDARD FORM using the information given. m = 2 and (3,-2) Start with slope-intercept form y 2x 8 -2x Now put into Standard form No LEADING NEGATIVES! Change all the signs of each term -2x 2x 3y 12 2x 3y 12 Ax By C If an equation is written in standard form, you can x & y intercepts to graph the equation use the _______________ quickly. 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 ( 2, 0) y 0 (0, 3) x 0 x-intercept is at ( 2, 0) y-intercept is at (0, 3) x 0 y0 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. 4 x 2 y 12 Plug in 0 for y x- intercept y-intercept 4 x 2 0 12 4x 12 4 Plug in 0 for x 4 x 3 x intercept 3,0 4 0 2 y 12 2 y 12 2 2 y 6 y intercept 0, 6 Example 4: Find the x & y intercepts of the following equations. B. 2 x 3 y 18 Plug in 0 for y x- intercept y-intercept 2 x 3 0 18 2x 18 2 Plug in 0 for x 2 x9 x intercept 9,0 2 0 3 y 18 3 y 18 3 3 y 6 y intercept 0, 6 Exit Card & Homework Exit Card: Write the equation in Standard Form (Ax + By = C) y = -2x – 4 Homework: WB p. 155-156 #2-32 (EVEN)