6th Grade Math Textbook, Fundamentals

y

x

 1 13

1

3

5

7

9

 3  1

(1,3)

(2,6)

rise  3 (3,9)

run  1

 &KDSWHU

13-7

change in x (run)

in changey (rise) 12 in.

1 in.

Ramp

Slope 

The slope of the wheelchair ramp will be.

Since the slope of a straight line is constant, you can calculate the

slope of a line using the coordinates of any two points on the line.

The slope of the graph y 3 xat the right is:

Slope  3

Check by using another pair of points on the line.

Slope  3

Slope is a rate of change and is constant for a line.

When a linear function is in the form of ykx, the

termk is called the. You can

say that yvaries directly with x.

The graph of a direct variation is a line through

the origin.

constant of variation

 3

 1

6  9

2  3

y 2 y 1

x 2 x 1

3

1

6  3

2  1

y 2 y 1

x 2 x 1

1

12

1

12

vertical change (rise)

horizontal change (run)

Key Concept

Slope

The slope of a line is the rate

of change.

Slope riserun

y 2 y 1

x 2 x 1

Slope

Objective To find the slope of a line

• To identify the four kinds of slope

Ms. Noriyama wants to build a wheelchair ramp. From researching
safety guidelines, she knows that the ramp should only rise 1 inch
for every 12 inches of ramp length. What will the slope of the
wheelchair ramp be?

 is the slant, or steepness, of a nonvertical line expressed

as a ratio. This ratio compares the vertical change in any two

points on the line to the horizontal change in the same two

points. The vertical change is called the , and the horizontal

change is called the. On the coordinate plane, for any two

points, (x 1 , y 1 ) and (x 2 , y 2 ), this ratio compares the change in the

y-coordinates, y 2 y 1 , to the change in the x-coordinates, x 2 x 1.

Slope 

So using the diagram below, Ms. Noriyama can find the

slope of the wheelchair ramp.

rise

run

run

rise

change in y

change in x

vertical change

horizontal change

y 2 y 1

x 2 x 1

Slope

Key Concept

Direct Variation

ykxor k, where x, k 0

y

x