Slope-Intercept Form

y=mx + b

Slope

Recall the three methods we can use to find slope.

bmxyxxyym

runrisem

12

12

Slope

And recall the 4 types of slope

Positive Slope Negative Slope No Slope 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.

bmxyxxyym

runrisem

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 monthper

…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 originalstartingwhere x = 0 (flat) feeone time cost of one item

You Try!

xy 4

623

xy

8 xy

5 xy

Find the slope and y-intercept for the following equations

xy 4

623

xy

8 xy

5 xy

0int,4 ym

6int,23

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 3/13)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.

145

145

21238

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)

bbb

bmxy

34 362

)9)(4(2

b

bb

b

b

b

bmxy

417

417 498

449424

492

)9(412

344 xy4

1741 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)

1728

68112

851713826

m

m

m

21728

28172826

17172826

)1(1

xy

xy

xy

xxmyy

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

21728

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 VariablesThe 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 change1728

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!