5-5 standard form. today, we will use to graph a line. the is the x-coordinate of a point where a...
TRANSCRIPT
5-5 STANDARD FORM
Today, we will use to graph a line.
The is the x-coordinate of a point where a graph crosses the x-axis. The y-intercept occurs when the value of is zero. The x-intercept occurs when the value of is zero.
Standard Form of a Linear Equation: _____________ where A, B, and C are , A is positive and A and B are not both zero.
When an equation is written in Standard Form it is easy to graph using the intercepts.
INTERCEPTS
x-INTERCEPT
xy
Ax By C REAL NUMBERS
Find the intercepts of the following graphs of the equation:
1) To find the x-intercept, substitute 0 in for y. Solve for x. 2) To find the y-intercept, substitute 0 in for x. Solve for y.
FINDING INTERCEPTS7x y
The x-intercept is 77x y
0 7x 7x
7x y 0 7y
7y
The y-intercept is 7
GRAPHING USING INTERCEPTSWhat is the graph of ? 1) x- intercept: 2) y- intercept:
3) Plot the points 4) Draw a line through the points.
4 3(0) 12x
4 3 12x y
4 12x 3x
3
4y 3 12y
4(0) 3 12y 4
(3,0) (0, 4)
HORIZONTAL AND VERTICAL LINESThe graph of is a horizontal line, and the graph of is a vertical line, where a and b are constants.
Given the equation graph the line: Rewrite in Standard Form: Name two points on the line:
Given the equation graph the line: Rewrite in Standard Form: Name two points on the line:
1x
0 1 4x y (0,4) (4,4)
4y
y b x a
( 1,0) ( 1,5)1 0 1x y
For all values of y, x = -1
For all values of x, y = 4
TRANSFORMING AN EQUATION TO STANDARD FORMWhat is written in standard form using integers?
1) Clear the fractions.
2) Rewrite so that the x and y values are on the same side of the equation: 3) Make the value of x positive:
34
5y x
35 4
5y x
5 3 20y x
3 5 20x y
1 3 5 20x y
3 5 20x y
TRANSFORMING AN EQUATION TO STANDARD FORMWhat is written in standard form using integers?
1) Use Distributive Property.
2) Rewrite so that the x and y values are on the same side of the equation: 3) Move the constants to the right side of the equation:
6 3( 1)y x
3 6 3x y
3 9x y
6 3 3y x
A festival sells ride tickets for $0.50 each and game tickets for $0.20 each. You have $5 to spend on tickets at the festival. Define variables: Equation: If you buy no game tickets how many ride tickets can you get? If you buy no ride tickets how many game tickets can you get? Find another combination:
USING STANDARD FORM AS A MODEL
ride
5
10
2 4 106
25x = ride ticketsy = game tickets
.5 .2 5x y 5 2 50x y
game
10x
25y
15
20
8
(8,5) (6,10) (4,15)
HOMEWORK: P. 354-355 #’S 8-34 EVEN
TRY THESEFind the intercepts of the following graphs of the equations:1)
2)
4 2 8x y 3 4 12x y 4 2(0) 8x
4 8x
2x
4y
2 8y 4(0) 2 8y
3 4(0) 12x
3 12x
4x
3(0) 4 12y 4 12y
3y
TRY THESE
Tell which form each linear equation is in:
1.
2.
3.
4.
5 ( 2)y x
2 5y x
10 2( 1)y x
2 4 12x y
Point-slope form
Point-slope form
Slope-intercept form
Standard form