Algebra Chapter 6 Review

1
Algebra Chapter 6 Review

• Finding slope of lines from
• Graphs
• Points
• Point - Slope and Standard Forms of Linear
  Equations
• Slope Intercept Equation
• X y intercepts
• Graphing Linear Equations
• Parallel Perpendicular Lines

2
Finding Slopes (m) of lines
Always read graph form Left to Right
If a line rises from left to right, the slope of
the line is positive. If it falls, then the slope
is negative.
Rise 6
Run 4
Slope (m) 6/4 3/2
3
Finding Slopes (m) of lines
Always read graph form Left to Right
Rise 2
If a line rises from left to right, the slope of
the line is positive. If it falls, then the slope
is negative.
Run 4
Slope (m) 2/4 -1/2
4
Slopes (m) of Special lines
Always read graph form Left to Right
Vertical lines have no slope or undefined
Horizontal lines have slope 0
5
Finding Slopes from points
When given two points we can use the slope
formula to find slope.
Example Find the slope of the line that passes
though points (3, 2) (4, 0).
6
Find slope from points

• Find the slope for the line through points (4, 9)
  (-2, 4).
• (4 - 9)/(-2 - 4) -5/-6 5/6
• Find the slope for the line through points (-4,
  -7) (2, 3).
• (3 - -7)/(2 - -4) 10/6 5/3

7
Writing Equations in Point-Slope Form
The basic form for the Point-slope equation is y
- y1 m(x x1) Where y x are part of the
final equation and y1, x1 m come from the
problem. Simply fill in given information to
write the equation. Example Write the
point-slope equation for the line through (3, 4)
with a slope of -3/4. y 4 -3/4(x 3)
8
Writing Equations in Point-Slope Form
Write the point-slope equation for the line
through (-3, 5) with a slope of 2. y 5 2(x
3) Write the point-slope equation for the line
through (6,1) (9, 3). Slope (-3 - -1)/(9 -
6) -2/3 y 1 -2/3(x 6) Or y 3 -2/3(x
9)
9
Writing Equations in Standard Form
The basic Standard Linear form is Ax By
C Where A, B C are integers (no fractions or
decimals). And A 0 (coefficient of x is
positive). Examples 4x 3y 9 is in Standard
form. -2/3x y 5 is not Standard form. y 7
is Standard form y 4x 5 is not Standard form.
10
Writing Equations in Standard Form

• Write the Standard Form for the line through (-3,
  5) with a slope of 2/3.
• Start with the point-slope form.
• y 5 2/3(x 3)
• 2) Distribute to remove parentheses.
• y - 5 2/3x 2
• 3) Move the x-term to the left side by addition
  or subtraction.
• -2/3x y 5 2
• 4) Move constant to right side by addition or
  subtraction.
• -2/3x y 7
• 5) Multiply by common denominator to eliminate
  fractions. Also, if x-term is negative, multiply
  by a negative to make x-term positive.
• -3(-2/3x y 7) 2x 3y -21

11
Write the Standard form equation for the line
through (2,2) and (4,7)

• Slope (7 2)/(4 2) 5/2
• Point-slope y - 2 5/2(x 2)
• y - 2 5/2x 5
• -5/2x y -3
• -2(-5/2x y -3)
• Standard Form 5x 2y 6

12
Slope Intercept Form of Linear Equation

• The slope-intercept for is written as
• y mx b
• Where m is slope and b is the y-intercept of the
  line. The y-intercept is where the line crosses
  the y-axis.

y-intercept 5
x-intercept 3
slope -5/3
Slope intercept form y -5/3x 5
13
Slope Intercept Form of Linear Equation

• Find the slope-intercept form of the line below.

y-intercept 5
slope 5/2
Slope intercept form y 5/2x 5
14
Finding Intercepts from equations
Find the x and y intercepts of the following
equations. To find the x-intercept, set y 0. To
find the y-intercept, set x 0. 3x 4y
6 y-intercept 3(0) 4y 6 4y 6 y
1.5 X-intercept 3x 4(0) 6 3x 6
x 2
15
Finding Intercepts from equations
Find the x and y intercepts of the following
equations. To find the x-intercept, set y 0. To
find the y-intercept, set x 0. x 2y 8 x
8, y 4 y -2/3x 3 x 4.5, y 3 y 5 x
none y 5
16
Graphing Linear equations
Standard Form use intercepts 3x 2y 6 x 2,
y -3
Slope - Intercept form Use the slope
intercept Y 2x 5 m 2, y-intercept 5
Point-slope form y 2 3(x 4) m 3, point
(-4, 2)
17
Graphing Linear equations
Graph the following lines y -2/3x 5 2x 6y
4 y 3 2(x 4) y 3x x -3 y -3
18
Parallel Perpendicular lines

• Lines that are parallel have equal slopes.
• Example all lines parallel to the line
  y 3x 5 have slopes of m 3.
• Perpendicular lines have slopes that are opposite
  (change signs) inverses (flip).
• If a line has slope of 3/4, line perpendicular to
  it would have slopes of -4/3.

19
Parallel Perpendicular Lines
Write the Standard form for the line parallel to
3x 5y 5 and passes through point
(4,3). Slope of given line m -A/B, m
-3/5 Slope of any parallel line would have slope
m -3/5 Point-slope of new line y 3 -3/5(x
4) y 3 -3/5x 12/5 3/5x y
-3/5 5(3/5x y -3/5) 3x 5y -3
20
Parallel Perpendicular Lines
Write the slope-intercept form for the line
perpendicular to y 5/2x 7 and passes
through point (3,8). Slope of given line m
5/2 Slope of any perpendicular line has slope m
-2/5 To find new line with m -2/5 (3,
8) 8 -2/5(3) b 8 -6/5 b b 46/5 slope
intercept for new line y -2/5x 46/5
21
Parallel Perpendicular Lines
Write the Standard form for the line
perpendicular to 4x 5y 6and passes
through point (-4, -6). Slope of given line m
4/5 Slope of any perpendicular line has slope m
-5/4 To find new line with m -5/4
(-4,-6) -6 -5/4(-4) b -6 5 b b
-11 slope intercept for new line y -5/4x
11 Standard form 5/4x y -11 5x 4y
-44
22
Find the x and y-intercepts of the following line.

• 5x 4y 9
• X 9/5 y 9/4

23
Write the standard form of the line parallel to
the line y 3/5x 3 and goes through point (5,3)

• Slope 3/5 3 3/5(5) b
• 3 3 b
• b 0
• y 3/5x

24
Write the slope intercept form of the line
perpendicular to the line 3x 4y 7 and goes
through point (0,3)

• Slope A/B m 3/4 3/4
• New slope -4/3
• 3 4/3(0) b
• b 3
• y 4/3x 3

25
Write the Standard equation for the line that
contains the point (-2,-3) and is parallel to
the line that passes through (2,2) (4,7).
Slope of given line (7 - 2)/4 - 2) 5/2 Slope
of desired line 5/2 New line -3 5/2(-2)
b -3 -5 b b 2 y 5/2x 2 -5/2x y
2 5x 2y -4
Write the Standard equation for the line that
contains the point (4,0) and is perpendicular to
the line above.
Slope of given line 5/2 Slope of desired line
-2/5 New line 0 -2/5(4) b 0 -8/5 b b
8/5 y -2/5x 8/5 2/5x y 8/5 2x 5y 8
26
Review Practice
27
Find the slope of the following lines

• 3x 4y 7
• 3/4
• Y 2x 4
• 2
• Through points (0,0) (4,2)
• -1/2

28
Graph the line x -3
29
Write the point slope equations for the line
through points (4,2) (-3,7)
y 2 -5/7(x 4) Or y 7 -5/7(x 3)
30
Graph the line y 4 -2/3(x 1)
31
Write the Standard Form for the line with slope
of ¾ and goes through point (3, -2)
3x 4y 17
32
Write the Slope intercept form of the line
through points (3,-2) (4, -2)
y -2
33
Find the value of r for the points (4,r) (r,7)
so that the line through them has a slope of 5.
r 4.5
34
Graph the line y 2/3x 4
35
Write the Standard form of the line through
points (4, -2) (4, -4)
x 4
36
Write the Standard form of the line perpendicular
to the line 4x 3y 4 and passes through the
point (4, -2)
3x 4y 4
37
Graph the line y 3 ½(x 3)
38
Write the Slope Intercept of the line parallel to
the line 4x 3y 4 and passes through the
point (4, -2)
y 4/3x 22/3
39
Find the x y intercepts of the line with the
equation 4x 5y 40
x 10, y -8
40
Graph the line 5x 3y -15
41
Write the Standard Form for the line with a slope
of 6/5 and point (-3,5)
6x 5y -43
42
Graph the line 4x 2y 8
43
Find the x y intercepts of the line with the
equation y 2/3x 6
x 9, y -6