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.

RememberAll we have

Learned about Lines

FORMULA FOR FINDING SLOPE

12

12

XX

YY

RUN

RISESLOPE

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

),(),( 2211 YXBandYXAlikelookThey

EXAMPLE

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

XX

YY

)4()10(

)8()4(

FORMULAINTOSUBSTITUTE

7

6

14

12

)4(10

84

)4()10(

)8()4(

SimplifyThen

Graphing Linear Equations

In 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.

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.

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.

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.

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

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

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

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.

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

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

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.

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

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

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

???

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

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

points (-2, 14) 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.

FIND THE SLOPE OF the LINE using the two points. M=????

??????

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) = -2

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.

???

Writing Equations – Type #32 = (-2) (4) + b

Solve the equation for b 2 = -8 + b

+8 +8 10 =b (ADD 8 to both sides)

To write an equation, you need two things:slope (m) = -2y – intercept (b) = 10y= -2 x +10

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

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

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

-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

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

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