Do Now 6/3/10
Take
out HW from last night.
Text
Copy
Positive slope
p. 407, #8-10, 12-30 evens
HW in your planner.
Text
p. 415, #10-12, 14-18 evens
Quiz sections 8.3-8.5 Tuesday
your notebook, identify
the slope of each colored line.
The black lines are the
x-and y-axis.
Undefined
Slope of 0
In
Negative slope
Homework
Text p. 407, #8-10, 12-30 evens

8) positive; 3/4
9) negative; -3/4
10) undefined
12) (0,-1) & (2, -1); m = 0
14) (6,0) & (0,3); m = -1/2
16) (3,0) & (3,5); m = undefined
18)
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20)
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22) 2
24) undefined
26) 7/8
28) -5
30) undefined
Objective

SWBAT graph linear equations
using slope-intercept form
Section 8.4 “The Slope of a Line”
SLOPEthe ratio of the vertical change (the rise) to
the horizontal change (the run) between
any two points on a line.
Slope =
rise = change in y
run
change in x
Slope Review
The slope m of a line passing through two points
( x1 , y1 ) and ( x2 , y2 ) is the ratio of the rise
change to the run.
y
m
( y2  y1 )
( x2  x1 )
run
( x2 , y2 )
rise
( x1 , y1 )
x
Section 8.5 “Graph Using SlopeIntercept Form”
SLOPE-INTERCEPT FORMa linear equation written in the form
y-coordinate
x-coordinate
y = mx + b
slope
y-intercept
Identifying Slope and the Y-Intercept
Slope of 3 means:
y = mx + b
y = 3x + 4
3 rise

1 run
 3 rise

 1 run
The equation is in the form y = m x + b. So, the slope
of the line is 3, and the y-intercept is 4.
3x + y = 2
Rewrite the equation in slope-intercept form by
solving for y.
y = 2 – 3x
y = -3x + 2
Is this in slope-intercept form?
The line has a slope of – 3 and a y-intercept of 2.
Identify the slope and y-intercept of the line with the
given equation.
3x – 3y = 12
Rewrite the equation in slope-intercept form by solving for y.
3x – 12 = 3y
Rewrite original equation.
y = 3x – 12
3
Divide 3 by equation.
y = x –4
Simplify.
ANSWER
The line has a slope of 1 and a y-intercept of –4.
Write an equation for the line.
y-intercept = -1
Slope = 1/1
y = mx + b
y=x–1
slope
Slope of
1/1 means:
y-intercept
1 rise

1 run
Graph an Equation Using the Slope-Intercept Form
Graph the equation
y = 2 - 2x.
y-axis
y  2  2x
5
4
Rewrite in slope-intercept form
3
y  2 x  2
2
1
slope
Slope of
-2 means:
y-intercept
 2 rise

1
run
OR
2 rise
Slope of

-2 means:
1 run
-6
-5
x-axis
-4
-3 -2 -1
0
-1
-2
-3
-4
-5
1
2
3
4
5
6
Graph an Equation Using the Slope-Intercept Form
Graph the equation
y = -3 + 2/3x.
y-axis
2
y  3  x
3
5
4
Rewrite in slope-intercept form
3
2
y  x 3
3
slope
Slope of
2/3 means:
y-intercept
2 rise

3 run
OR
 2 rise
Slope of

2/3 means:
 3 run
2
1
-6
-5
x-axis
-4
-3 -2 -1
0
-1
-2
-3
-4
-5
1
2
3
4
5
6
Graph Using Slope and the Y-Intercept
Graph the equation 2x + y = 3.
STEP 1
Rewrite the equation in slope-intercept form.
y = – 2x + 3
Slope of -2 means:
( 2) rise

1
run
STEP 2
Identify the slope and the y-intercept.
m=–2
and
b =3
STEP 3
Plot the point that corresponds to the
y-intercept,(0, 3).
STEP 4
Use the slope to locate a second point on the line. Draw a line
through the two points.
Graph Using Slope and the Y-Intercept
Graph the equation 3y – 2x = 3.
STEP 1
Rewrite the equation in slope-intercept form.
y =
Slope of 2/3 means:
2 rise

3 run
2 x
+1
3
STEP 2
Identify the slope and the y-intercept.
m = 2/3
and
b =1
STEP 3
Plot the point that corresponds to the
y-intercept,(0, 1).
STEP 4
Use the slope to locate a second point on the line. Draw a line
through the two points.
Parallel Lines
two lines in the same plane are parallel if
they never intersect. Because slope gives the
rate at which a line rises or falls, two lines with
the SAME SLOPE are PARALLEL.
y = 3x + 2
y = 3x – 4
Perpendicular Lines
two lines in the same plane are perpendicular if
they intersect at right angles. Because slope gives
the rate at which a line rises or falls, two lines with
slopes that are NEGATIVE RECIPROCALS are
PERPENDICULAR.
½ and -2 are
negative reciprocals.
4/3 and -3/4
are negative reciprocals.
y = -2x + 2
y = 1/2x – 4
Determine which of the lines are parallel.
Find the slope
of each line.
Line a: m =
–1– 0
–1– 2
Line b: m = – 3 – (–1 )
0 – 5
– 5 – (–3)
Line c: m =
–2–4
–1
1
= –3 =
3
–2
2
= –5 =
5
–2
1
= –6 = 3
Line a and line c have the same slope, so they are parallel.
Guided Practice
Worksheet Form C odds
Homework
Text p.247 #4-38 even