writing and graphing slope intercept form

of 29 /29
Objective The student will be able to: 1)Graph linear equations in slope- intercept form. 2)write equations using slope- intercept form. 3) identify slope and y- intercept from an equation.

Upload: guestd1dc2e

Post on 18-May-2015

10.141 views

Category:

Education


3 download

TRANSCRIPT

Page 1: Writing and Graphing slope intercept form

ObjectiveThe student will be able to:

1) Graph linear equations in slope- intercept form.

2) write equations using slope-intercept form.

3) identify slope and y-intercept from an equation.

Page 2: Writing and Graphing slope intercept form

Remember

Page 3: Writing and Graphing slope intercept form

FORMULA FOR FINDING SLOPE

21

21

12

12

YY

XX

YY

XX

RUN

RISESLOPE

The formula is used when you know two points of a line.

),(),( 2211 YXBandYXAlikelookThey

EXAMPLE

Page 4: Writing and Graphing slope intercept form

Find the slope of the line between the two points (-4, 8) and (10, -4)

If it helps label the points. 1X 1Y2X 2Y

Then use the formula

12

12

YY

XX

)8()4(

)4()10(

FORMULAINTOSUBSTITUTE

6

7

12

14

)8(4

410

)8()4(

)4()10(

SimplifyThen

Page 5: Writing and Graphing slope intercept form

Graphing Linear Equations

In Slope-Intercept Form

Page 6: Writing and Graphing slope intercept form

We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line.

In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.

Page 7: Writing and Graphing slope intercept form

y 2x 1

y x 4

y 32

x 2

These equations are all in Slope-Intercept Form:

Notice that these equations are all solved for y.

Page 8: Writing and Graphing slope intercept form

Just by looking at an equation in this form, we can draw the line (no tables).

•The constant is the y-intercept.

•The coefficient is the slope.

y 2x 1

y x 4

y 3

2x 2

Constant = 1, y-intercept = 1.

Coefficient = 2, slope = 2.

Constant = -4, y-intercept = -4.

Coefficient = -1, slope = -1.

Constant = -2, y-intercept = -2.

Coefficient = 3/2, slope = 3/2.

Page 9: Writing and Graphing slope intercept form

The formula for Slope-Intercept Form is:

y mx b;• ‘b’ is the y-intercept.

• ‘m’ is the slope.

On the next three slides we will graph the three equations:

y 2x 1, y x 4, y 3

2x 2

using their y-intercepts and slopes.

Page 10: Writing and Graphing slope intercept form

y 2x 1

1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.

up 2

right 1 up 2

right 1

Page 11: Writing and Graphing slope intercept form

1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1.

right 1down 1

right 1

y x 4

down 1

Page 12: Writing and Graphing slope intercept form

1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2.

right 2

up 3

y 3

2x 2

right 2

up 3

Page 13: Writing and Graphing slope intercept form

Sometimes we must solve the equation for y before we can graph it.

2x y 3

2x y ( 2x) ( 2x) 3

y 2x 3

The constant, b = 3 is the y-intercept.

The coefficient, m = -2 is the slope.

Page 14: Writing and Graphing slope intercept form

1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.

right 1down 2

right 1

down 2

y 2x 3

Page 15: Writing and Graphing slope intercept form

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

Page 16: Writing and Graphing slope intercept form

Writing Equations

When asked to write an equation, you need to know two things – slope (m) and y-intercept (b).

There are three types of problems you will face.

Page 17: Writing and Graphing slope intercept form

Writing Equations – Type #1Write an equation in slope-intercept form of the

line that has a slope of 2 and a y-intercept of 6.

To write an equation, you need two things:

slope (m) =

y – intercept (b) =

We have both!! Plug them into slope-intercept form

y = mx + b

y = 2x + 6

2

6

Page 18: Writing and Graphing slope intercept form

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

Page 19: Writing and Graphing slope intercept form

Writing Equations – Type #2Write an equation of the line that has a slope of 3

and goes through the point (2,1).

To write an equation, you need two things:

slope (m) =

y – intercept (b) =

We have to find the y-intercept!! Plug in the slope and ordered pair into

y = mx + b

1 = 3(2) + b

3

???

Page 20: Writing and Graphing slope intercept form

Writing Equations – Type #21 = 3(2) + b

Solve the equation for b

1 = 6 + b

-6 -6

-5 = b

To write an equation, you need two things:

slope (m) =

y – intercept (b) =

y = 3x - 5

3

-5

Page 21: Writing and Graphing slope intercept form

Writing Equations – Type #3Write an equation of the line that goes through the points (-2,

1) and (4, 2). To write an equation, you need two things:

slope (m) =y – intercept (b) =

We need both!! First, we have to find the slope. Plug the points into the slope formula.

Simplify2 1

4 ( 2)m

??????

1

6m

Page 22: Writing and Graphing slope intercept form

Writing Equations – Type #3Write an equation of the line that goes through the

points (-2, 1) and (4, 2). To write an equation, you need two things:

slope (m) =y – intercept (b) =

It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use?

I’m using (4, 2) because both numbers are positive.2 = (4) + b

1

6???

1

6

Page 23: Writing and Graphing slope intercept form

Writing Equations – Type #3

2 = (4) + bSolve the equation for b

2 = + b

To write an equation, you need two things:

slope (m) =

y – intercept (b) =

1

62

32

3

11

3b

2

3

1

6 11

3

1 11

6 3y x

Page 24: Writing and Graphing slope intercept form

Write an equation of the line that goes through the points (0, 1) and (1, 4).

1. y = 3x + 4

2. y = 3x + 1

3. y = -3x + 4

4. y = -3x + 1

Page 25: Writing and Graphing slope intercept form

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 = -7

Page 26: Writing and Graphing slope intercept form

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

3m =

b = 0

2

3

2

3

m = 0b = 5

Page 27: Writing and Graphing slope intercept form

-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

3m =

b = -2

5

3

Page 28: Writing and Graphing slope intercept form

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 = -1

Page 29: Writing and Graphing slope intercept form

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