# 1.2 Linear Equations in Two Variables

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1.2 Linear Equations in Two Variables
Writing linear equations

How do we define Slope

Rise over Run The change of y over the change in x
Given point (x1, y1) and (x2, y2)

Find Slope through two points
Lets the points by (6, 10) and (5, -3) So the slope would be So the slope is or just 13

Slope-intercept form y = mx + b
m is for slope; b is the y intercept We do we use m for Slope and b for the intercept? What is the slope of

Horizontal lines and Vertical lines
Horizontal line have zero slopes. Vertical line have undefined slopes. Why?

m = When (y1) – (y2) = 0, there is no rise in the line. The fraction would equal zero When (x1) – (x2) = 0, it makes the fraction undefined. The dominator of a fraction can near be zero.

What is the difference of a ratio and a rate or rate of change
Ratio have the same units Rate have different units

Writing Linear Equations in 2 variables
Point-Slope form Lets write equation using the points (580,50) and (625,47) The slope would be

Using one of the two points
Using the point (580, 50)

The General form a line Ax + By + C = 0
A, B and C are not all zero or fractions Multiply both sides by 15 to get rid of fractions, then add x and subtract 580.

Parallel and Perpendicular Lines
Parallel lines have the same slope Perpendicular line have negative reciprocal slopes

Test for Parallel or Perpendicular
Given 2 lines with sets of points Line1: (0,8) and (4, 5) Line 2: (6, 10) and (0, 2) Find the slopes of each line

Line 1: has slope Line 2: have slope So what are the lines?

Homework Pages 21-24 # 2,8,12,16,22,26,30,34,38,40,46,48,52,56, 60,64,68,72,76,80,84,88

Homework Page 21 – 26 # 13, 25, 41, 51, 79, 89, 101, 107, 117, 123, 134