Transcript Week 4 Algebra and Functions

Math Strategies
Algebra and Functions
Order of Operations:
• Parentheses or other grouping
symbols
• Exponents and roots
• Multiplication and division from
Left to Right
• Addition and Subtraction from
Left to Right
Solving Equations
• When solving equations, it is important to
keep the sides balanced.
– To undo addition, SUBTRACT
– To undo subtraction, ADD
– To undo multiplication, DIVIDE
– To undo division, MULTIPLY
Solving Expressions
• Find the value of the expression if x = 7 and
y = -2.
( x  y )( x  y )
  x 2  ( x  y )  y 0 
Writing Expressions
• Vocabulary
– Sum, increased by, more than => addition
– Difference, less than, decreased =>
subtraction
– Product, times, multiplied => multiplication
– Quotient, divide => division
– Double, twice, two times => multiply by 2
Writing Expressions
• The product of a number and 7 increase
by 2
• 6 less than the quotient of 25 and a
number
• The difference of 16 and the product of a
number and 22
Practice
• The sum of twice a number and 34
• 17 less than the product of a number and
12
• The quotient of a number and 5 decreased
by 7
Practice
• When a = 3 and b = -4, what is the value
of the expression?
3a  2b
2
b
ab
Examples
• Find the value of f in 3f – 2 = 16.
• Solve for x.
x
48
2
Example Word Problem
• Kevin is 16 years old. The sum of his age
and his brother’s is 4 less than double
Kevin’s age. How old is Kevin’s brother?
Example Word Problem
• Julie is thinking of two consecutive
numbers. If you add 5 to both numbers,
the sum is 21. Find the smaller number.
Practice
• Solve for y. 3y + 6 = 15
• Find the value of k. k
3
6  7
• What is the value of m? 5m + 7 = 37
• Georgia is 12 years old. The sum of her age
and her sister’s is 2 less than double Georgia’s
age. Find Georgia’s sister’s age.
Practice
• The sum of two numbers is 88. The
second number is four times the first
added to 5. Write the two equations.
Solve.
Graphing
• Plotting a point.
y
– (x, y)
– Remember to go over
x and up/down y.
• Plot
–
–
–
–
A (3, 5)
B (-4, 7)
C (5, -2)
D (-2, -3)
x
Practice
y
Plot
– A (-6, 3)
– B (0, 0)
– C (5, 0)
– D (-4, -2)
– E (0, -9)
– F (4, 4)
x
Graphing
• Slope =
rise change in y y 2  y1


run change in x x2  x1
• x-intercept = value where the equation
crosses the x-axis. Let y = 0
• y-intercept = value where the equation
crosses the y-axis. Let x = 0
Find the Intercept
• Find the y-intercept: 5x + 12y = -48
• Find the x-intercept: -½ x + ¾ y = -6
Slope
• Negative Slope:
• Positive Slope:
• Parallel Slope: Slope
is the SAME as the
original line
• Perpendicular Slope:
slope is the negative
reciprocal of the
original line (change
the sign and flip the
slope)
y
x
Two Special Slopes
• Any line parallel to the y-axis has an
UNDEFINED slope.
• Any line parallel to the x-axis has 0 slope.
Slope
• What is the slope of the line drawn
through (3, 0) and (-1, -4)?
• Find the Slope of the line perpendicular to
the above slope.
Practice
• What is the slope of the line y = -3?
• What is the slope of the line between the
two points (1, -1) and (3, 5)?
• What is the slope of the line 6x + 3y = -3?
Forms of Equations
• Standard form: Ax + By = C
• Slope-intercept: y = mx + b where
m = slope and b = y-intercept. b is
the starting point on the y-axis.
Graph:
• 2x + 6y = 4
• Find the slope of the line parallel to the
above line.
Graph
• Graph y = x3
y
x
Practice
• Graph
y = -3x2
y
x
3y = -2x + 1
Practice
• Graph
x = -8
y
x
y=7