6-1 Slope

Slope is a measure ofsteepness.

The letter “m” isused to represent

slope.

4 Types of Slope

PositiveNegative

Zero

Undefinedor

No Slope

Slope is sometimesreferred to as the

“constant rate of change”between 2 points.

The constant rate of change can be

written as = Change in the Dependent Variable Change in the Independent Variable

Dependent = Y valueIndependent = X value

Since slope is a constant rate of change, always

look for a number or pattern that

repeats.

X Y

1 -4

2 -1

3 2

4 5

So what pattern do you see that the y-values follow? What happens every time? That’s the slope of the table!

If given 2 points on a line, you may findthe slope using theformula m = y2 – y1

x2 – x1

(the change in y divided by the change in x)

The formula may sometimes be written

as m =∆y . ∆x

What does ∆ stand for?change

m = y2 – y1

x2 – x1

Find the slope of the line through the

points (3,7) and (5, 19).x1y1 x2 y2

m = 19 – 7

5 – 3 m = 12 2

m = 6

(3, 4) and (-6, -2)

m = -2 – 4 -6 – 3

m = -6 -9

m = ⅔

m = y2 – y1

x2 – x1

(0, -5) and (4, 3)

m = 3 – -5 4 – 0

m = 8 4

m = 2 or 2/1

m = y2 – y1

x2 – x1

What if thenumerator is 0?

m = 0

What if thedenominator is 0?

m = undefined or no slope

Slope is also found bym = rise

run

If given the graphof a line, find the

slope by using the“triangle” method to

find the rise over run.

rise = 4

run = 5

m= rise

run

m= 4/5

rise = 2

run = -5

m= rise

run

m= - 2/5

Recap today’s lesson:• Slope is the steepness of a line or constant rate of change.

• m represents slope• Slope can be found different ways

• Rise over Run• Y2 – Y1 X2 – X1