Review of Slope and the slope intercept formula

y=mx+b

change in ym slope

change in x

What is the slope of the line that contains these points?

Point A (0,3)

Point B (2,2)

+2

+3 A

Brise

sloperun

The slope of this line is..

+2

+3 A

B

3

2slope

riseslope

run

What is the slope of this line?

-2

+2

riseslope

run

What is the slope of this line?

-2

+2

2

2slope

21

2

What is the slope of this line?

+2

+1

riseslope

run

What is the y -intercept of this line?

• In other words, at what coordinate does the line cross the y-axis?

• y intercept is -5

y axis

x axis

What is the y -intercept of this line?

• At what coordinate does the line cross the y-axis?

• y intercept is 0

y axis

x axis

What is the y -intercept of this line?

• At what coordinate does the line cross the y-axis?

• y intercept is +5

y axis

x axis

What is the y -intercept of this line?

• At what coordinate does the line cross the y-axis?

• y intercept is -2

y axis

x axis

How to write the equation

for this line -2

+221

2m

y mx b

5b

1 5y x

Write an equation for this line.

+2

+3

3

2slope

1b

31

2y x

y mx b

What is the slope of this line?

+2

+1

1

2slope

0b

10

2y x 1

2y x

y mx b

Write an equation for this line.

y axis

x axis1

55

y x

Write an equation for this line.

y axis

x axis2

25

y x

What is the slope of this line?

0slope

2y

What is the slope of this line?

slope undefined

4x

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)

…without graphing.

A B

change in yslope

change in x

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.

2 1

2 1

y ym

x x

Find the slope when you are given two points from a line.

Point 1 (2,-3)

Point 2 (3,4)

Use the formula for slope.

Remember, m=slope.

2 1

2 1

y ym

x x

4 3

3 2m

77

1m

Using the same points, but labeling them #2 and #1

Point 2 (2,-3)

Point 1 (3,4)

Use the formula for slope.

Remember, m=slope.

2 1

2 1

y ym

x x

3 4

2 3m

77

1m

Find the slope when you are given the following two points from a line.

Point C (-2,-6)

Point D (3,5)

Use the formula for slope.

Remember, m=slope.

2 1

2 1

y ym

x x

5 6

3 2m

11

5m

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.

Remember, m=slope.

2 1

2 1

y ym

x x

4 6

1 9m

2 1

8 4m

Review Part Three

Finding the equation from two given points from the line

Find the Linear Equation

Point E (9,6)

Point F (1,4)

You found the slope (m) to be ¼.

Insert ¼ as m in the slope intercept formula.

Let’s pick the x and y values from Point F and insert them into the formula. (1,4)

1

4y x b

14 (1)

4b

14

4b

334b

Write the Linear Equation

Point E (9,6)

Point F (1,4)Now use the value for

the slope (m) and y-intercept (b) to rewrite the formula.1

4 (1)4

b

14

4b

334b

1 33

4 4y x

Write the Linear EquationUse points R and S

Point R (5,3)

Point S (1,7)

Reminder: (x,y)

Substitute the values for Point R.

3 = -1(5) + b

3 = -5 + b

(Add 5 to both sides)

1y x b

8 b

7 3 4

1 5 4m

y mx b 1 8y x

8y x

Write the Linear EquationUse points W and T

Point W (-4,-3)

Point T (-2,-6)

Substituting the values for Point T…

-6 = -3/2(-2) + b

-6 = +6/2 + b

(Subtract 3 from both sides)

3

2y x b

9 b

6 3 3

2 4 2m

y mx b

39

2y x

Review Part Four

Find the x and y intercepts

Given: y = -3x + 12

• Use zero as the x value.y = -3(0) + 12

y = 12

Replace (x,y) with 0 and 12.

(0,12)

• Use zero as the y value.0 = -3x + 12Subtract 12 from both sides

- 12 = -3xDivide both sides by -3- 12 = -3x -3 -3

-4 =xReplace (x,y) with -4 and

0.(-4,0)

Given: y = -4x + 8Find the x and y intercepts.

• Use zero as the x value.

• Then use zero as the y value.

x y

0 ?

? 0 x intercept is (0,-8)y intercept is (2,0)

Assignment

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