Calculating Slope of a Line

What you should have remembered from Gr. 9!

See…your teachers told you you’d see it again…..and???

They were correct!!

The slope of a line describes the following:• The steepness of a line• The vertical change relative to the

horizontal change• The change in the y-direction relative to

the change in the x-direction

x

y

Horizontal change (run)

(∆x)

Vertical change (rise)

(∆y)

• The slope of a linear equation (straight line) is the same everywhere.

• A line with positive slope rises from left to right.

• A line with negative slope falls from left to right.

x

y

Input: x Output: y = x + 1 (x, y)

0 1 (0, 1)

1 2 (1, 2)

2 3 (2, 3)

3 4 (3, 4)

Use points (0,1) and (2,3) to calculate the slope.

102

13slope

2

1 3

slope = ∆y ∆x

= y2 – y1

x2 – x1

• Very steep lines have large slopes, while relatively flat lines have small slopes.

More facts:

x

y

Question: Which of the three lines above have the largest slope?

Answer: The blue line!

Line of Best Fit• When calculating slope of a data set, your

data may not be perfectly linear.• You must draw a line of best fit!• Draw a line through the data points.

Line of Best Fit• Your line should pass through as many points as

possible and follow the general trend of the coordinates.

• To calculate slope, pick two coordinates that are far apart and touching/close to your line of best fit.

Slope= ∆y∆x

= y2 – y1

x2 – x1

= 2.4 – 6.88.4 – 2.0

= -4.4 6.4 = -.6875 = -.69

(x1, y1)

(x2, y2)

• Animation (regression)

• The slope of a line can be calculated from :

a table

a graph

two coordinate points on the line

using the formula :

.12

12

xx

yyslope

) y,(x and ),( 2211 yx

1

2

3

run

riseSlope