Do Now

1. Solve the equation

2. Find the x-intercept and the y-intercept of the equation

€

2(1 − x) + 3x = −4(x + 2)

€

5x + y = 25

€

2 − 2x + 3x = −4 x − 8

2 + x = −4 x − 8+4x +4x

2 + 5x = -8-2 -2

5x = -10

5 5

x = -2

5x + (0) = 25

5x = 25

x = 5

(5,0)

5(0) + y = 25

y = 25 (0,25)

S

Section 5.1Slope-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 + bm represents the slope

b represents the y-intercept

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 = (0,-7)

Find the slope and y-intercept.

2) y = x

y = mx + b

y = x + 0

3) y = 5

y = mx + b

y = 0x + 5

2

3 m =

b = (0,0)

2

32

3

m = 0b = (0,5)

HORIZONTAL LINE

-3 -3 -3

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

y = x - 25

3

m =

b = (0,-2)

5

3

Write it in slope-intercept form. (y = mx + b)

2y + 2 = 4x

2y = 4x - 2

y = 2x - 1

Find the slope and y-intercept. 5) 2y + 2 = 4x

2 2 2 m = 2b = (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 4 2y x 2 2

2 4 2y x 2 2 2

(divide both sides by 2 to get y alone)

2 4 2y x

(now simplify all fractions)2 1

2 1y x

When an equation is in slope-intercept form:

What is the slope? ____________

2 1y x Now look at the equation below……

What is the intercept? ____________

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Step 1: Look at the y-intercept and plot where the graphs cross the “y” axis.

Now look at the graph of the line.

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.

*** Easy ***

5y = 10x + 15Convert to Slope-Intercept Form:

(divide both sides by 5 to get y alone)

(now simplify all fractions)

y = 2x + 3 BRAVO!!

5 10 15y x 5 5

5 10 15y x 5 5 5

*** Now Try this Convert to

Slope-Intercept 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 (divide both sides by -3 to get y alone)

(now simplify all fractions)

y = 3x + 4

-3 -3

-3y = -9x - 12-3 -3 -3

Slope = 3

Intercept = 4

Wow, you’re good at this!!

*** medium ***

21x – 7y =14Convert to Slope-Intercept Form:

(subtract both sides by 21x)

-7y = -21x + 14(now divide both sides by -7)

y = 3x – 2

(simplify all fractions)

21 -21xx

7 - 7 -7

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

*** Now Try this Convert to Slope-

Intercept Form ***

What is the slope? ____________

What is the intercept? ____________

2y + 26 = -6x(subtract both sides by 26)

2y = -6x - 26(now divide both sides by 2

y = -3x - 13

(simplify all fractions)

You are a math wizard!

*** Check Your Answer ***

26 -26

2 2 2

Slope-Intercept Fromy = 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

Ex 1 Write the slope-intercept form using

Slope-intercept form

Replace m with and b with –4.

Answer: The equation is

Write an Equation Given Slope and y-intercept

Ex 2 Write the slope-intercept form using

Answer: The equation is

Slope-intercept form

Replace m with –4 and b with –16.

Write an Equation Given slope and y-int.

Create an equation using the given information:

1. Slope = 3y-intercept = (0,-6)

2. Slope = -2y-intercept = (0,7)

3. Slope = 2/5y-intercept = (0,-10)

€

y = 3x − 6

€

y = −2x + 7

€

y =2

5x −10

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 = −4x

Now look at this graph and create the equation

m = 2/3

b = (0,-3)

€

y =2

3x − 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)

m =

y = x - 3

3

2

x

y

+2

+3

3

2

Example 2

b = (0,1)

m =

y = x + 1

1

2

x

y

-12

1

2

Example 3

b = (0,4)

m = 0/1= 0

y = 0x + 4, y = 4

x

y

Write an equation of a lineA

BC

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-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?

y = mx + by = 2x + (-4)y = 2x -4

Let’s try some examples! Write the equation of a

line with a slope of -2 and a y-intercept of 6.

y = mx + b y = -2x + 6

Write the equation of a line with a slope of -4/3 and a y-intercept of 1.

y = mx + b 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