Algebra 1 Common Core Student Edition, Grade 8-9

The graphs of th e ordered pairs (time, distance) in Problem 1

lie on a line, as show n at th e right. The relationship b etw een

tim e an d distance is linear. W hen d ata are linear, th e rate of

change is constant.

N otice also th a t th e rate of change found in P roblem 1 is

just the ratio of the vertical change (or rise) to th e h orizontal

change (or run) betw een two points on th e line. The rate of

change is called th e slope of th e line.

vertical change rise

horizontal change run

Distance Marched

slope

Pjgn
What do you need to
find th e slope?
You need to find the rise
and run. You can use the
graph to count units of
rise and units o f run.

Finding Slope Using a G raph

What is the slope of each line?

up

2 u n its

r_ I _^

V

right 3

units

4

\

,1) X

• '' I

-2 _ 1)

A 4

slope = jun, rise

_ 2

3

The slope of th e line is 3. The slope of th e line is — 5.

vj Go t I t? 2. W hat is th e slope of each line in p arts (a) a n d (b)?

c. R e a so n in g In p a rt (A) of Problem 2, pick two new points o n th e line to

find th e slope. Do you get th e sam e slope?

Notice th at th e line in p a rt (A) of P roblem 2 has a positive slope an d slants upw ard from

left to right. The line in p a rt (B) of P roblem 2 has a negative slope an d slopes dow nw ard

from left to right.

PowerAlgebra.com | Lesson 5-1 Rat e o f Ch an g e an d Sl o p e"^295