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Practice converting Practice converting linear equations linear equations into Slope-Intercept into Slope-Intercept Form Form It’s easier than you think… It’s easier than you think…

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Page 1: Slope intercept

Practice converting Practice converting linear equations into linear equations into Slope-Intercept FormSlope-Intercept Form

Practice converting Practice converting linear equations into linear equations into Slope-Intercept FormSlope-Intercept Form

It’s easier than you think…It’s easier than you think…

Page 2: Slope intercept

Slope intercept form is:

y = mx + b

Our main goal is to get the y alone on one side of the

equation

Page 3: Slope intercept

Convert Into Convert Into Slope-InterceptSlope-Intercept Form FormConvert Into Convert Into Slope-InterceptSlope-Intercept Form 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

Page 4: Slope intercept

When an equation is in slope-When an equation is in slope-intercept form:intercept form:

When an equation is in slope-When an equation is in slope-intercept form:intercept form:

What is the slope? ____________

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

What is the intercept? ____________

Page 5: Slope 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 Step 1: Look at the y-intercepty-intercept and and plot plot where the graphs cross the “y” where the graphs cross the “y” axis.axis.

Now look at the graph of the line. Now look at the graph of the line.

Step 2: Use the Step 2: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot.

Step 3: Draw a line Step 3: Draw a line through both points. through both points. Be sure to extend pass Be sure to extend pass point and put arrow at point and put arrow at both ends.both ends.

Page 6: Slope intercept

*** Easy ***

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

(divide both sides by 5 to get y alone)

(now simplify all fractions)

y = 2x + 3

5 10 15y x 5 5

5 10 15y x 5 5 5

Page 7: Slope intercept

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

y = 2x + 3

Page 8: Slope intercept

*** 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? ____________

Page 9: Slope 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

Page 10: Slope intercept

y = 3x + 4

Slope = 3

Intercept = 4

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Because there is no room to move up 3 we will have to move down 3 and to the LEFT 1

Page 11: Slope intercept

*** 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

Page 12: Slope intercept

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? ____________

Page 13: Slope intercept

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

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

y = -3x - 13

(simplify all fractions)

*** Check Your Answer ***

26 -26

2 2 2

Page 14: Slope intercept

The word “intercept” means to cross.

Page 15: Slope intercept

x-interceptx-intercept - the point (ordered pair) where a line crosses the x-axis.

y-intercepty-intercept - the point (ordered pair) where a line crosses the y-axis.

Page 16: Slope intercept

Find the x and y intercepts of the line below.

x

y

-3 -2 -1 1 2 3

3

2

1

-1

-2

-3

Page 17: Slope intercept

Find the x and y intercepts of the line below.

x

yWhere does

the line cross the x-axis?

x-intercept is (-2,0)

-3 -2 -1 1 2 3

3

2

1

-1

-2

-3

Page 18: Slope intercept

Find the x and y intercepts of the line below.

x

Where does the line cross the y-axis?

x-intercept is (-2,0)

y-intercept is (0,2) -3 -2 -1 1 2 3

Sometimes, this is written as x-intercept = -2 and y-intercept = 2.

3

2

1

-1

-2

-3

y

Page 19: Slope intercept

Find the x and y intercepts of the line below.

x-3 -2 -1 1 2 3

y3

2

1

-1

-2

-3

Page 20: Slope intercept

Find the x and y intercepts of the line below.

x

Where does the line cross the x-axis?

x-intercept is (1,0)

-3 -2 -1 1 2 3

y3

2

1

-1

-2

-3

Page 21: Slope intercept

Find the x and y intercepts of the line below.

x

Where does the line cross the y-axis?

x-intercept is (1,0)

y-intercept is (0,3)

-3 -2 -1 1 2 3

y3

2

1

-1

-2

-3

Page 22: Slope intercept

Find the x and y intercepts of the line below.

x-3 -2 -1 1 2 3

y3

2

1

-1

-2

-3

Page 23: Slope intercept

Find the x and y intercepts of the line below.

x

Where does the line cross the x-axis?

x-intercept is (-1,0)

y3

2

1

-1

-2

-3

-3 -2 -1 1 2 3

Page 24: Slope intercept

Find the x and y intercepts of the line below.

x

Where does the line cross the y-axis?

x-intercept is (-1,0)

y-intercept is (0,½ )

-3 -2 -1 1 2 3

y3

2

1

-1

-2

-3

Page 25: Slope intercept

Sometimes, we must find the intercepts without a graph.

x

y

-3 -2 -1 1 2 3

3

2

1

-1

-2

-3

Page 26: Slope intercept

Sometimes, we must find the intercepts without a graph.

We use the equation of the line.

Page 27: Slope intercept

To find the x intercept, let y = 0

To find the y intercept, let x = 0Substitute 0 for y.

Substitute 0 for x.

Page 28: Slope intercept

Find the x and y intercepts of the graph of the equation 2x – 5y = 10.

x-intercept

1 052 yx

1 0)0(52 x

1 002 x

1 02 x2

2

5x

y-intercept1 052 yx

1 05)0(2 y

1 050 y

5

5

2y

1 05 y

The x-intercept is (5,0).

The y-intercept is (0,–2).