Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.

Slope-Intercept Form

y=mx + b

Slope

Recall the three methods we can use to find slope.

bmxy

xx

yym

run

risem

12

12

Slope

And recall the 4 types of slope

Positive Slope Negative Slope Slope of Zero Undefined Slope

Increases Left to Right

Decreases Left to Right

Horizontal Line Vertical Line

y = 3x + 2 y = - 3x + 2 y = 3 x = 5

Slope

There are 3 methods we can use to find slope!

Each one works best for certain situations.

bmxy

xx

yym

run

risem

12

12

Remember this guy?

This is Slope Intercept Form.

We can use this equation to find the slope of a line and the y-intercept.

bmxy Remember this guy?

The slope is a constant but it is always affected by

something. The slope tells you the rate of change over each interval or time or an occurrence.

initial

…a yearevery

each …a month

per

…a day

The y-intercept is a constant.

This means that it is the starting point in a word problem, or a value that does not change and is not affected by

anything happening within the word problem.

initial originalstarting

where x = 0 (flat) fee

one time cost of one item

You Try!

xy 4

62

3 xy

8 xy

5 xy

Find the slope and y-intercept for the following equations

xy 4

62

3 xy

8 xy

5 xy

0int,4 ym

6int,2

3 ym

8int,1 ym

5int,1 ym

How did you do?

Graphing

When given an equation like y = -3x + 2

You can graph the line by following these simple steps:

When given an equation like y = -3x + 2

You can graph the line by following these simple steps:

1)Plot the y-intercept.(0,2)

When given an equation like y = -3x + 2

You can graph the line by following these simple steps:

1)Plot the y-intercept.

Notice that the slope is negative so the line must run from upper left to lower right!

(0,2)

(1,-1)

When given an equation like y = -3x + 2

You can graph the line by following these simple steps:

1)Plot the y-intercept.2)Use the slope to trace (rise / run) to the next point on the line. -3 is actually - 3/1

Notice that the slope is negative so the line must run from upper left to lower right!

(0,2)

When given an equation like y = -3x + 2

You can graph the line by following these simple steps:

1)Plot the y-intercept.2)Use the slope to trace (rise / run) to the next point on the line. 3 is actually 3/1

3)Connect the points with a line.

(1,-1)

(0,2)

Notice that the slope is negative so the line must run from upper left to lower right!

Review Problems

Given: The slope of a line is -2 and the y-intercept is 3. Write the equation of the line in slope-intercept form.

The information provided is enough for you to write the equation. m = -2, b = 3 and slope-intercept form isy = mx + b.

32 xy

Write the equation of the line in slope-intercept form that passes through the points: (2,-3) and (-12,-8).To write an equation in slope-intercept form we need the slope. 1.Use the ordered pairs to find the slope.

14

5

14

5

212

38

212

)3(8

m

Write the equation of the line in slope-intercept form that passes through the point (9,-2) and is

a)Parallel to y = -4x+7b)Perpendicular to y = -4x+7

Parallel Perpendicular

1. Slope of the parallel is -42. m = -4 and (9,-2)

1. Slope of the perpendicular is

¼ .

2. m = ¼ and (9,-2)

b

b

b

bmxy

34

362

)9)(4(2

b

b

b

b

b

b

bmxy

4

17

417

498

44

9424

4

92

)9(4

12

344 xy4

17

4

1 xy

Celia is out picking strawberries. She had 26 strawberries in her bucket after she had been picking for 17 minutes. She is now finished after spending 85 minutes picking. She has 138 strawberries.

Write an equation to model the number of strawberries, n, Celia picked per minute, t.

1. Independent and Dependent Variables

2. After you write the ordered pairs, find m.

3. Use the values to find the equation.

(Let’s practice with point-slope formula this time)

The number picked depends on the time spent picking.

Number is dependent on time, so the ordered pairs will look like: (t, n)

(17, 26) and (85, 138)

17

2868

1128517

13826

m

m

m

217

28

2817

2826

1717

2826

)1(1

xy

xy

xy

xxmyy

So, what does this mean?(let’s “interpret” a look on the next slide)

217

28 xy

We determined that the number of strawberries she had depended on the amount of time she had been picking.

The slope, 28/17, is the change in “y” or dependent value, which is n in this case over the change in “x” or the independent value, which is t in this case.

So we can say that

1. Independent and Dependent Variables

The number picked depends on the time spent picking.

Number is dependent on time, so the ordered pairs will look like: (t, n)

minutesin change

esstrawberri of #in change

17

28

Interpret slope : for every 17 minutes she picked 28 strawberries.

Or, if we find the unit rate by dividing, we get 1.647, which means for every 1 minute she picked about 1.647 strawberries.

Interpret y-intercept : she began with -2 strawberries. This is not realistic!