Download 4.4 and 4.5

• A surveys ask high school freshman
whether they would be willing to pay $5 for
their yearbooks. Out of the 225 freshman
surveyed, 198 said “yes”. What percent of
the freshman said “yes”?
88%
Objective
The student will be able to:
1) Graph linear equations in slope- intercept
form.
2) write equations using slope-intercept form.
3) identify slope and y-intercept from an
equation.
Review Part Two
Finding Slope without Graphing
When you are given two points you
may have to find the slope...
Point A (2,-3)
Point B (3,4)
change  in  y
slope 
change  in  x
…without graphing.
A
B
Find the slope when you are given
two points from a line.
Point A (2,-3)
Point B (3,4)
Use the formula for
slope.
Remember, m=slope.
y2  y1
m
x2  x1
Find the slope when you are given
two points from a line.
Point 1 (2,-3)
Point 2 (3,4)
y2  y1
m
x2  x1

Use the formula for
slope.
Remember, m=slope.
4 3
m
3 2
7
m 7
1
Using the same points, but labeling
them #2 and #1
Point 2 (2,-3)
Point 1 (3,4)
y2  y1
m
x2  x1

Use the formula for
slope.
3 4
m
23

Remember, m=slope.
7 
m   7
1
Find the slope when you are given
the following two points from a line.
Point C (-2,-6)
Point D (3,5)
y2  y1
m
x2  x1

Use the formula for
slope.
Remember, m=slope.
5 6
m

3 2
11
m
5
Find the slope when you are given
the following two points from a line.
Point E (9,6)
Point F (1,4)
Use the formula for
slope.
y2  y1
m
x2  x1
46
m
1 9

Remember, m=slope.
2
1
m  
8
4
Remember
FORMULA FOR FINDING
SLOPE
The formula is used when you know two
points of a line.
They look like A( X1 , Y1 ) and B( X 2 , Y2 )
RISE
Y2  Y1
SLOPE 

RUN X 2  X 1
EXAMPLE
Find the slope of the line between the two points (-4, 8) and (10, -4)
If it helps label the points.
X1 Y1
X2
Y2
Then use the
formula
Y2  Y1
(4  (8)
X 2  X 1 SUBSTITUTE INTO FORMULA (10)  (4)
(4)  (8)  4  (8)  12
6
Then Simplify



(10)  (4)
10  4
14
7
Graphing Linear Equations
In Slope-Intercept Form
We have already seen that linear
equations have two variables and when
we plot all the (x,y) pairs that make the
equation true we get a line.
In this section, instead of making a
table, evaluating y for each x, plotting
the points and making a line, we will
use The Slope-Intercept Form of the
equation to graph the line.
These equations are all in SlopeIntercept Form:
y  2x  1
y  x  4
3
y x2
2
Notice that these equations are all
solved for y.
Just by looking at an equation in this form, we
can draw the line (no tables).
•The constant is the y-intercept.
•The coefficient is the slope.
y  2x 1
Constant = 1, y-intercept = 1.
y  x  4
Constant = -4, y-intercept = -4.
3
y x2
2
Coefficient = 2, slope = 2.
Coefficient = -1, slope = -1.
Constant = -2, y-intercept = -2.
Coefficient = 3/2, slope = 3/2.
The formula for Slope-Intercept Form is:
y  mx  b;
• ‘b’ is the y-intercept.
• ‘m’ is the slope.
On the next three slides we will graph the three
equations:
3
y  2x  1, y   x  4, y  x  2
2
using their y-intercepts and slopes.
y  2x 1
right 1
right 1 up 2
up 2
1) Plot the y-intercept as
a point on the y-axis. The
constant, b = 1, so the yintercept = 1.
2) Plot more points by
counting the slope up the
numerator (down if
negative) and right the
denominator. The
coefficient, m = 2, so the
slope = 2/1.
y  x  4
1) Plot the y-intercept as
a point on the y-axis. The
constant, b = -4, so the yintercept = -4.
down 1
right 1
down 1
right 1
2) Plot more points by
counting the slope up the
numerator (down if
negative) and right the
denominator. The
coefficient, m = -1, so the
slope = -1/1.
3
y x2
2
right 2
up 3
right 2
up 3
1) Plot the y-intercept as
a point on the y-axis. The
constant, b = -2, so the yintercept = -2.
2) Plot more points by
counting the slope up the
numerator (down if
negative) and right the
denominator. The
coefficient, m = 3/2, so the
slope = 3/2.
Sometimes we must solve the equation
for y before we can graph it.
2x  y  3
2x  y  (2x)  (2x)  3
y  2x  3
The constant, b = 3 is the y-intercept.
The coefficient, m = -2 is the slope.
y  2x  3
1) Plot the y-intercept as
a point on the y-axis. The
constant, b = 3, so the yintercept = 3.
down 2
right 1
down 2
right 1
2) Plot more points by
counting the slope up the
numerator (down if
negative) and right the
denominator. The
coefficient, m = -2, so the
slope = -2/1.
Important!!!
This is one of the big concepts in
Algebra 1. You need to thoroughly
understand this!
Slope – Intercept Form
y = mx + b
m represents the slope
b represents the y-intercept
Writing Equations
When asked to write an equation, you
need to know two things – slope (m)
and y-intercept (b).
There are three types of problems you
will face.
Writing Equations – Type #1
Write an equation in slope-intercept form of the
line that has a slope of 2 and a y-intercept of 6.
To write an equation, you need two things:
slope (m) = 2
y – intercept (b) = 6
We have both!! Plug them into slope-intercept
form
y = mx + b
y = 2x + 6
Write the equation of a line that has
a y-intercept of -3 and a slope of -4.
1. y = -3x – 4
2. y = -4x – 3
3. y = -3x + 4
4. y = -4x + 3
Writing Equations – Type #2
Write an equation of the line that has a slope of 3
and goes through the point (2,1).
To write an equation, you need two things:
slope (m) = 3
y – intercept (b) = ???
We have to find the y-intercept!! Plug in the
slope and ordered pair into
y = mx + b
1 = 3(2) + b
Writing Equations – Type #2
1 = 3(2) + b
Solve the equation for b
1=6+b
-6 -6
-5 = b
To write an equation, you need two things:
slope (m) = 3
y – intercept (b) = -5
y = 3x - 5
Writing Equations – Type #3
Write an equation of the line that goes through the
points (-2, 1) and (4, 2).
To write an equation, you need two things:
slope (m) = ???
y – intercept (b) = ???
We need both!! First, we have to find the slope.
Plug the points into the slope formula.
2 1
m
4  (2)
1
Simplify m 
6
Writing Equations – Type #3
Write an equation of the line that goes through the
points (-2, 1) and (4, 2).
To write an equation, you need two things:
1
slope (m) = 6
y – intercept (b) = ???
It’s now a Type #2 problem. Pick one of the ordered
pairs to plug into the equation. Which one looks
easiest to use?
I’m using (4, 2) because both numbers are positive.
1
2 = (4) + b
6
Writing Equations – Type #3
1
2 = (4) + b
6
Solve the equation for b
2
2= +b
3
2
2
 
3
3
1
1 b
3
To write an equation, you need two things:
1
slope (m) =
6
1
y
y – intercept (b) = 1
3
1
1
x 1
6
3
Write an equation of the line that goes
through the points (0, 1) and (1, 4).
1.
2.
3.
4.
y = 3x + 4
y = 3x + 1
y = -3x + 4
y = -3x + 1
To find the slope and y-intercept of
an equation, write the equation in
slope-intercept form: y = mx + b.
Find the slope and y-intercept.
1) y = 3x – 7
y = mx + b
m = 3, b = -7
Find the slope and y-intercept.
2
2) y = x
3
y = mx + b
2
y= x+0
2
m=
3
b=0
3
3) y = 5
y = mx + b
y = 0x + 5
m=0
b=5
Find the slope and y-intercept.
4)
5x - 3y = 6
Write it in slope-intercept form. (y = mx + b)
5x – 3y = 6
-3y = -5x + 6
-3
-3 -3
y=
5
3
x-2
5
m=
3
b = -2
Find the slope and y-intercept.
5) 2y + 2 = 4x
Write it in slope-intercept form. (y = mx + b)
2y + 2 = 4x
2y = 4x - 2
2
2
2
y = 2x - 1
m=2
b = -1
Find the slope and y-intercept of
y = -2x + 4
1.
2.
3.
4.
m = 2; b = 4
m = 4; b = 2
m = -2; b = 4
m = 4; b = -2
Home Education!!!
• Section 4.5 pg.247-248
#4-16(EVEN), 17-19, 26, 28, 30,
33, 40
Next class Quiz #5 Sec. 4.3 &
4.4!