Do Now
1.
Solve the equation
2(1  x)  3x  4(x  2)
2  2x  3x  4 x  8
2  x  4 x  8
+4x

2.
+4x
2 + 5x = -8
-2
-2
5x = -10

5
x = -2
5
Find the x-intercept and the y-intercept of the equation
5x  y  25
5x + (0) = 25
5x = 25
x=5
(5,0)
5(0) + y = 25
y = 25
(0,25)
Section 5.1
Slope-Intercept Form
y = mx + b
S
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
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To find the slope and y-intercept of an
equation, write the equation in slopeintercept form: y = mx + b.
Find the slope and y-intercept.
1) y = 3x – 7
y = mx + b
m = 3, b = (0,-7)
Find the slope and y-intercept.
2)
2
y= x
3
y = mx + b
2
y =3 x + 0
3) y = 5
y = mx + b
y = 0x + 5
m= 2
3
b = (0,0)
HORIZONTAL LINE
m=0
b = (0,5)
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
y=
-3
5
x
3
-3
-2
5
m=
3
b = (0,-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 = (0,-1)
Find the slope and y-intercept of
y = -2x + 4
1. m = 2; b = 4
2. m = 4; b = 2
3. m = -2; b = 4
4. m = 4; b = -2
Convert Into Slope-Intercept Form
2 y  4x  2
(divide both sides by 2 to get y alone)
2 y  4x  2
2
2
(now simplify all fractions)
2 y  4x  2
2
2
2
2
1
y  2x 1
When an equation is in slope-intercept
form:
Now look at the equation below……
y  2x 1
What is the slope? ____________
What is the intercept? ____________
Now look at the graph of the line.
Step 1: Look at the y-intercept and plot
where the graphs cross the “y” axis.
Step 2: Use the slope
(rise/run) to determine the
next point and plot.
Step 3: Draw a line through
both points. Be sure to extend
pass point and put arrow at
both ends.
5
4
3
2
1
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
2
3
4
5
*** Easy ***
Convert to Slope-Intercept Form:
5y = 10x + 15
(divide both sides by 5 to get y alone)
5 y  10 x  15
5
5
5 y  10 x  15
5
5
5
(now simplify all fractions)
y = 2x + 3 BRAVO!!
*** Now Try this Convert to SlopeIntercept Form ***
-3y = -9x - 12
Step 1: divide both sides by -3 to get y alone
Step 2: Simplify all fractions
Step 3: Write your equation in y = mx + b
What is the slope? ____________
What is the intercept? ____________
*** Check Your Answer ***
-3y = -9x - 12
-3 -3
(divide both sides by -3 to get y alone)
(now simplify all fractions)
-3y = -9x - 12
-3 -3 -3
y = 3x + 4
Slope = 3
Intercept = 4
Wow, you’re good
at this!!
*** medium ***
Convert to Slope-Intercept Form:
21x – 7y =14
(subtract both sides by 21x)
21x
-21x
(now divide both sides by -7)
-7y = -21x + 14
7 - 7 -7
y = 3x – 2
(simplify all fractions)
*** Now Try this Convert to SlopeIntercept Form ***
2y + 26 = -6x
Step 1: Subtract both sides by 26
Step 2: Divide both sides by 2 to get y by itself
Step 3: Simplify all fractions
What is the slope? ____________
What is the intercept? ____________
*** Check Your Answer ***
2y + 26 = -6x
(subtract both sides by 26)
26
-26
(now divide both sides by 2
2y = -6x - 26
2
2 2
(simplify all fractions)
y = -3x - 13
You are a math wizard!
Slope-Intercept From
y = mx + b
What are the two things
we see/use in this form?
1. m = Slope
2. b = y-intercept
Could you make an
equation if I gave you:
m=2
b = (0,6)
y  2x  6
Write an Equation Given Slope and y-intercept
Ex 1
Write the slope-intercept form using
Slope-intercept form
Replace m with
Answer: The equation is
and b with –4.
Write an Equation Given slope and y-int.
Ex 2
Write the slope-intercept form using
Slope-intercept form
Replace m with –4 and
b with –16.
Answer: The equation is
Create an equation using the
given information:
1. Slope = 3
y-intercept = (0,-6)
y  3x  6
2. Slope = -2
y-intercept = (0,7)
y  2x  7

3. Slope = 2/5
y-intercept = (0,-10)

2
y  x 10
5
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
Now look at this graph and
create the equation
m = -2/1
b = (0,2)
y  2x  2
Now look at this graph and
create the equation
m = 1/1
b = (0,2)
y  x 2
Now look at this graph and
create the equation
m = -4/1
b = (0,0)
y  4 x
Now look at this graph and
create the equation
m = 2/3
b = (0,-3)
2
y  x3
3
Now look at this graph and
create the equation
m = undefined
b = none
x  3
Now look at this graph and
create the equation
m = none
b = (0,-2)
y  2
Write an equation given two points
on a graph
b = (0,-3)
3
m=
2
3
y= x-3
2
+2
+3
y
x
Example 2
b = (0,1)
2
m
-1
= 1
2
y = 1 x + 1
2
y
x
Example 3
b = (0,4)
x
m = 0/1= 0
y = 0x + 4, y = 4
y
Write an equation of a line
A
B
C
Write the Equation of a Line from a
Graph
 Where does the line cross the
y-axis?
◦ At the point (0, -4)
◦ The y-intercept is -4.
 What is the slope of the line?
◦ The graph also crosses the x-
y = mx + b
y = 2x + (-4)
y = 2x -4
axis at (2, 0).
◦ We can use the slope formula
to find our slope.
m = -4 – 0 = -4 = 2
0 – 2 -2
We know our slope is 2 and our
y-intercept is -4, what is the
equation of our line?
Let’s try some examples!
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Write the equation of a line
with a slope of -2 and a yintercept of 6.
S
Write the equation of a line
with a slope of -4/3 and a yintercept of 1.
S
y = mx + b
S
y = mx + b
S
y = -2x + 6
S
y = (-4/3) + 1
Using a graph
 Where does the line cross
the y-axis?
◦ At the point (0, 2)
◦ So the y-intercept b is 2.
 The line also passes
through the point (3, 0).
 We can use these points to
find the slope of the line.
How? What formula do
we use?
◦ Using the slope formula, we
find that the slope m is -2/3.
◦ Write the equation of the
line.


y= mx + b
y = (-2/3)x + 2