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…

Slope intercept form is:

y = mx + b

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

equation

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

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? ____________

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.

*** 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

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

y = 2x + 3

*** 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

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

*** 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)

*** Check Your Answer ***

26 -26

2 2 2

The word “intercept” means to cross.

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.

Find the x and y intercepts of the line below.

x

y

-3 -2 -1 1 2 3

3

2

1

-1

-2

-3

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

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

Find the x and y intercepts of the line below.

x-3 -2 -1 1 2 3

y3

2

1

-1

-2

-3

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

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

Find the x and y intercepts of the line below.

x-3 -2 -1 1 2 3

y3

2

1

-1

-2

-3

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

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

Sometimes, we must find the intercepts without a graph.

x

y

-3 -2 -1 1 2 3

3

2

1

-1

-2

-3

Sometimes, we must find the intercepts without a graph.

We use the equation of the line.

To find the x intercept, let y = 0

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

Substitute 0 for x.

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).