Download Chapter 4 - Windsor C

Chapter 4
Algebra I and Concepts
Day 1, Section 4-1: Graphing in SlopeIntercept Form
Slope-Intercept Form: Any equation written in the
form y = mx + b
m:
b:
Which of the following are in slope intercept form?
Are any in standard form?
a) 4y = 2x + 6
b) y = 3x – 5
c) 2x – 5y = 12
Day 1, Section 4-1: Graphing in SlopeIntercept Form
Ex) Identify the slope and the y-intercept of the
following equations
a) y = ½x – 5
b) y = x + 7 c) 2x – 3y = 12
Ex) Write an equation of a line in slope-intercept
form, given the slope and the y-intercept
a) Slope: 4, y-intercept: -2 a) m = 6, b = 12
Day 1, Section 4-1: Graphing in SlopeIntercept Form
Steps to Graphing an equation in slope-intercept
form. Ex) y = 2 x - 4
3
1) Plot the
________________
2) Count the slope
________ over _________,
And plot a second point
3) Draw a line connecting
The 2 points
Day 1, Section 4-1: Graphing in Slope-Intercept
Form
Slope Movement
Positive Numbers: UP/RIGHT
Negative Number: DOWN/LEFT
Ex) Graph the following equations using slopeintercept form method
a) y = -4 x + 2
b) y = 5x + 8
c) 5x – 3y = 15
5
Day 2: Section 4-1, Horizontal and Vertical
Lines
Graphing Horizontal Lines
Equations look like this:
y = a number
(there is NO x variable!)
To Graph:
1) Draw a horizontal line through
that number
Graph y = -2
Graphing Vertical Lines
Equations look like this:
x = a number
(there is NO y variable)
To Graph:
1) Draw a vertical line through
that number
Graph x = 6
Day 2: Section 4-1, Horizontal and
Vertical Lines
Graph the following lines. First determine if the line
is horizontal, vertical, or oblique.
1) y = 4
2) y = -2x + 4
3) x = -1
Day 2: Section 4-1
Write an equation in slope-intercept form for
the graph pictured
1)
2)
3)
Day 1, Section 4-2: Writing Equations
in Slope-Intercept Form
Writing equations in slope-intercept form when given the
slope and a point.
Steps (USE y = mx + b)
Example: slope = 2, (-3, 5)
1) Plug the slope in for m
2) Plug the point in for
x and y
3) Solve for b
4) Write the equation
Using the given m and
The b you just found
Day 1, Section 4-2: Writing Equations
in Slope-Intercept Form
Write a equation for the line using the
information given. Use slope-intercept form
1) (3, 1), slope 2
2) (-1, 4), slope -1
Day 2: Section 4-2, Writing Equations
in Slope Intercept Form
Write an equation in slope intercept form of a line
through the 2 points: (3, 1) and (2, 4)
Steps (use y = mx + b)
Example:
1) Use the 2 points and the
Slope formula to find m
2) Use m and one point and
Plug into y = mx + b to find b
3) Re-write the equation
Day 2: Section 4-2, Writing Equations
in Slope Intercept Form
Write an equation in slope intercept form of a
line through the 2 points:
a) (-4, -2) and (-5, -6)
b) (-1, 12) and (4, -8)
Day 1: Section 4-3, Point-Slope Form
Point-Slope Form: given a point (x1, y1 ) , and the
slope, an equation can be written such that
y - y1 = m(x - x1 )
Name
Equation
When to use it
Slope-Intercept Form
Point-Slope From
Standard Form
Only when converting from a
previous form
Day 1: Section 4-3, Point-Slope Form
Ex) Write an equation in point-slope form for a
line that passes through the point (3, -2) and has
a slope of ¼ . Then graph the line.
Day 1: Section 4-3, Point-Slope Form
Identify the slope and the given point in each of
the equations that are in point-slope form.
1) y – 3 = 10(x + 4)
2) y + 5 = -2(x +6)
3) y + 1 = x – 5
4) y – 8 = -x
Day 1: Section 4-3, Point-Slope Form
Graph the equations that are in point-slope form.
1) y – 2 = 3(x + 4)
2) y + 8 = -½ (x – 1)
Day 2: Section 4-3, Re-writing
equations
Ex) Write
-2
y -1 = (x - 5) in standard form
3
Ex) Write y + 3 = 3 (x +1) in slope-intercept form
2
Day 2: Section 4-3, Write an Equation
using a Picture of the Graph
Write an equation for each line in point-slope
form and then convert the equation to slopeintercept form AND standard form.
Day 1: Section 4-4, Parallel Lines
Parallel Lines – lines that do not intersect and have
the SAME SLOPE!
Which of the following lines are parallel? Note: you
must be able to identify the slope in each equation!
a) y = 2x + 3
b) 2x + y = 10
c) y - 2x = 5
d) y -1 = 2(x + 7)
e) 8x + 2y = 12
Day 1: Section 4-4, Parallel Lines
Write an equation in slope-intercept form for the line
that passes through (-3, 5) and is parallel to the line y =
2x – 4
Steps
Example
1) Find the slope you need
(remember about slopes
Of parallel lines!)
2) Use m and the point to
Plug into y = mx +b and
Solve for b
3) Re-write the equation
Day 1: Section 4-4, Parallel Lines
Ex1) Write an equation in slope-intercept form
for a line parallel to y = 3x – 5 and through the
point (4, -3)
Ex2) Write an equation in slope-intercept form
for a line parallel to y = -½x + 6 and through the
point (-4, 2)
Day 2: Section 4-4 Perpendicular Lines
Opposite Reciprocals – 2 numbers whose product is
-1. Flip and switch the sign!
Perpendicular Lines - Lines that intersect to form a
right angle. Perpendicular lines have slopes that are
opposite reciprocals.
Ex) Find the opposite reciprocals of the following
numbers
a) 3
b) -5
c) ½
d) -¾
Day 2: Section 4-4 Perpendicular Lines
Write an equation in slope-intercept form for the line
that passes through (8, 2) and is perpendicular to the
line y = -4x + 5
Steps
Example
1) Find the slope you need
(remember about slopes
Of perpendicular lines!)
2) Use m and the point to
Plug into y = mx +b and
Solve for b
3) Re-write the equation
Day 2: Section 4-4 Perpendicular Lines
Ex1) Write an equation in slope-intercept form for a
line perpendicular to y = x + 4 and through the point
(3, -2)
Ex2) Write an equation in slope-intercept form for a
-3
line perpendicular to y = x + 4 and through the
4
point (-2, 3)
Day 2: Section 4-4, Comparing Lines
Determine if the lines are parallel,
perpendicular, or neither.
1) y = -2x
2) -3x + 4y = 8
2x + y = 3
3) 3x + 5y = 10
5x - 3y = -6
-4x + 3y = -6
4)
2x + 7y = -35
4x +14y = -42
Section 4-5, Scatterplots
Scatterplot – a graph showing the relationship
between a set of data with 2 variables
Section 4-5, Scatterplots
Ex) What kind of correlation does the graph
have? Describe its meaning.
Section 4-5, Scatterplots
Section 4-5: Scatterplots
Section 4-5: Scatterplots