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Section 1.2

- Linear Equations in Two Variables

What you should learn

- How to use slope to graph linear equations in two

variables - How to write linear equations in two variables
- How to use slope to identify parallel and

perpendicular lines - How to use linear equations in two variables to

model and solve real-life problems

Slope

Slope describes the direction of a line.

Slope

Why is this needed?

- If x1 ? x2, the slope of the line through the

distinct points (x1, y1) and (x2, y2) is

Guard against 0 in the denominator

Find the slope between (-3, 6) and (5, 2)

Rise

-4

-1

Run

8

2

Find the slope between(-3, 6) and (5, 2)

Find the Slope

Green

(3, 9)

Blue

(11, 2)

Red

(5, -2)

Find the slope between (5, 4) and (5, 2).

STOP

This slope is undefined.

Find the slope between (5, 4) and (5, 2).

Rise

-2

Undefined

Run

0

Find the slope between(5, 4) and (-3, 4).

STOP

This slope is zero.

Find the slope between (5, 4) and (-3, 4).

Rise

0

Zero

Run

-8

From these results we can see...

- The slope of a vertical line is undefined.
- The slope of a horizontal line is 0.

Graph the line that goes through (1, -3) with

(1,-3)

Using Slope to Graph

- Graph the line that contains (4, 5) and has a

slope of 3/2.

(8, 11)

(6, 8)

(4, 5)

Using Slope to Graph

- Graph

(0, 8)

(4, 5)

(8, 2)

Slope

Point-Slope

Slope

Point

Slope Intercept

Slope

Y-intercept

Standard Form of a Line

Parallel Lines

- Two distinct nonvertical lines are parallel if

and only if their slopes are equal. - That is,

Parallel

- Find the slope-intercept form of the line that

passes through (2,1) parallel to - 2x 3y 5.

Perpendicular

- Find the slope-intercept form of the line that

passes through (2,1) perpendicular to - 2x 3y 5.

Homework

- Page 21
- 1, 9-27 odd 39- 45 odd, 51-79 odd
- 87- 95 odd, 105 - 113 odd, 117

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