= -9= 0 = -4 = -5/6 g. take out homework. show me your work. check
TRANSCRIPT
Warmup:
Evaluate the following if: f(x) = 2x 5 g(x) = x-2 3-x
1. f( 2) 2. g(2)
3. f
2
1 4. ( 3)
= -9 = 0
= -4
= -5/6
g
Take out Homework.Show me your work.Check.
Homework Check:
Complete all parts of each question.
1. Each table below shows a different input-output relationship.
a) Find the rate of change in each table. Explain how you found this value.
b) For each table, find the output value that corresponds to an input value of 0. What is this value called? c) Use your results from 1a and 1b to write an equation in y = mx + b form. d) Use the words NOW and NEXT to write the rules that represent the data in the tables. a) b) c) d)
Input Output
0 -6
1 -2.5
2 1
3 4.5
4 8
a) b) c) d)
Input Output
-1 -7
0 1
3 25
5 41
7 57
a) b) c) d)
Input Output
-5 -35
5 -21
10 -14
20 0
35 21
m = 3.5
-6, y-intercept
Next = Now + 3.5; starting at -6
y = 3.5x - 6
m = 8
1, y-intercept
NEXT = NOW + 8; starting at 1
y = 8x + 1
m = 1.4
-28, y-intercept
NEXT = NOW +1.4; starting at -28
y = 1.4x - 28
2. You can represent linear relationships with a graph, a table of values, or an equation. Here are two linear relationships. Give all the other ways to show each relationship. a) For the line graphed below, complete the table of values and write the equation
Table of values: x y
Equation:
0 1
2 2
4 3
6 4
y = ½ x + 1
b) For the table of values below, graph and write the equation of the line.
x y
-2 2
-1.5 1.5
0 0
3 -3
Graph:
Equation:
y = -x
Objective: To learn to -practice putting equations into y = mx + b form from other forms and from identified intercepts.
Transforming Standard Form and Intercepts into Slope Intercept Form:
Transforming Standard Form and Intercepts into Slope Intercept Form:
Graph the line whose x-intercept is 3 and y-intercept is –1.
Write the equation of this line.
y = 1/3 x - 1
Transforming Standard Form and Intercepts into Slope Intercept Form:
For each of the following problems, graph the line given the intercepts then write the equation of the line. 1. x-intercept: -2 2. x-intercept: 1 3. x-intercept: -4 y-intercept: -4 y-intercept: 3 y-intercept: 1
Equation __________ Equation ____________ Equation ____________
y = -2x - 4 y = -3x + 3 y = ¼ x + 1
Transforming Standard Form and Intercepts into Slope Intercept Form:
Standard Form and I ntercepts
Another Option for Graphing Linear Equations!! Standard Form – Standard f orms give you another option f or graphing equations. I nstead of transforming the equation to slope-intercept f orm (y=mx+b), you can use Standard Form to solve f or the x- and y-intercepts, then graph. Example 1: Find the x-intercept and y-intercept of the line 2x + 3y = 6. Use the intercepts to graph the equation. Find the x-intercept: Find the y-intercept:
(___, 0)
2x + 3(0) = 6
2x = 6
x = 3
3
(0, ___) 2(0) + 3y = 6
3y = 6y = 2
2
Ax + By = C
Transforming Standard Form and Intercepts into Slope Intercept Form:
You Try: Find the x-intercept and y-intercept of the line x – y = -3. Use the intercepts to graph the equation. Find the x-intercept: Find the y-intercept:
Draw in manually
Transforming Standard Form and Intercepts into Slope Intercept Form:
Solve each equation f or y, then graph. Example 1: 6y – 12x = 24
Draw in manually
Transforming Standard Form and Intercepts into Slope Intercept Form:
Example 2: 20 – 2y = 4x
Draw in manually
Transforming Standard Form and Intercepts into Slope Intercept Form:
Example 3: y + 2x - 3= 5x
Draw in manually
Transforming Standard Form and Intercepts into Slope Intercept Form:
Example 4: -15y + 2x = 30Draw in manually
You Try: Solve each equation for y, then graph 1) 2y – 5x = 16 2) y - x = 6 3) 3x + y = 5
4) y – 2x + 4 = 10 5) 20x + 4y = 8 6) 9y + 3x = 1
Draw in manually after the students try these.
HW: Transforming to Slope Intercept Homework
Assignment: