Download Section 5-1- Slope A. Definitions 1. Slope is the steepness of a line

Section 5-1- Slope
A. Definitions
1. Slope is the steepness of a line.
2. Slope is the vertical rise over the horizontal
run.
change in y (rise)
3. Slope =
change in x (run)
Ex 1: Determine the slope of each graph.
a.)
b.)
4. Formula for slope is m =
( y2 − y1 )
.
( x2 − x1 )
5. Lines
a. A vertical line has a slope that is
undefined.
b. A horizontal line has a slope of zero.
Ex 2: Find the slope of
the line that passes
through (-3, 2) and (5, 5).
Ex 3: Determine the
slope of a line that
passes through (2, -5)
and (7, -10).
Ex 4: Determine the value of r so that the line
3
through (r, 6) and (10, -3) has a slope of − .
2
HW: Algebra 5-1 p. 260-262
15-37 odd, 41-44, 50-52, 57, 59-60, 65-76, 77-85 odd
Section 5-3 - Slope-Intercept form
A. Slope-Intercept Form
1. The slope intercept form of an equation is
y = mx + b , where m = slope and b = y-intercept.
Ex 1: Write an equation whose slope is 2 and the yintercept is -5.
Ex 2: Write the equation of
the line in the graph.
2
Ex 3: Graph y = − x + 5 .
3
Ex 4: Graph 5 x + 4 y = 8 .
HW: Algebra 5-3 p. 275-277
15-39 odd, 40-42, 45-46, 51-52, 58-60, 62-67
Section 5-4 Writing Equations in Slope-Intercept Form
A. Write an equation given the Slope and One Point.
Ex 1: Write an equation of the line that passes
through (2, -3) with a slope of ½.
(solve for b) y = mx + b
B. Write an equation given two points.
Ex 2: The table of ordered pairs shows the
coordinates of two points on the graph of a function.
Which equation describes the function?
x y
A. 5 y = 12 x − 16
-3 -4
B. y = 4 x − 16
-2 -8
C. y = −4 x + 16
D. y = −4 x − 16
Ex 3: In the middle of the 2004 season, Ichiro Suzuki
was on track to break the single season hits record.
After 36 games, he had 58 hits. After 128 games,
Suzuki had 207 hits. Write a linear equation to
estimate the number of hits for any number of games
he played in.
HW: Algebra 5-4 p. 284-285
11-33 odd, 40-43, 46-47, 49-50, 53-62
5-5 - Writing Equations in Point-Slope Form
A. Point-slope Form
1. An equation can be written in point-slope form,
which is y − y1 = m( x − x1 ) .
Ex 1: Write the point-slope form of an equation that
−3
passes through (-2, 0) with a slope of
.
2
B. Forms of Linear Equations
1. Standard Form: Ax + By = C .
2. Slope-intercept form: y = mx + b .
3. Point-slope form: y − y1 = m( x − x1 ) .
5
Ex 2: Write y + 3 = − ( x − 2) in standard form.
4
4
Ex 3: Write y − 5 = ( x − 3) in slope-intercept form.
3
Ex 4: Write the equation of a line in slope intercept
form that passes through (4, 3) and (6, -2).
HW: Algebra 5-5 p. 289-291
15-51 odd, 55-57, 66, 72-87
Section 5-6 - Parallel and Perpendicular Lines
A. Parallel lines
1. Two lines are parallel if they are in the same
plane but do not intersect.
2. Parallel line have the same slope.
Ex 1: Write the slope intercept form of an equation
that passes through (4, -2) and is parallel to the graph
1
of y = x − 7 .
2
B. Perpendicular lines
1. Two lines are perpendicular if the product of their
slopes is -1.
Ex 2: Given A(5,5), B(8, 4), C(7, 1) and D(0, 0).
Determine if AC ⊥ BD .
Ex 3: Write the slope intercept form of an equation
that passes through (4, -1) and is perpendicular to the
graph of 7 x − 2 y = 3 .
HW: Algebra 5-6 p. 296-297
13-37 odd, 42-44, 48-49, 50-54, 55-59 odd