Analyzing Linear Relations Chapter 6

Chapter 6
Slope
 Steepness of a line
 The change in the y coordinate divided by the change




in x
Ϫy
Ϫx
Ratio of the rise over run
Vertical change divided by horizontal change
Given any two coordinate points,
m = (y₂- y₁)
( x₂ - x₁)
Slope Examples
 Find the slope of a line in graph form
 Find the slope of a line when given two points
 Find a missing coordinate when a different point, the
slope is given, and one coordinate of the second point.
Slopes can be ….
 Positive
 Change in y over change in x both have the same sign
 As x increases y increases
 Positive correlation
 Negative
 Change in y over change in x have different signs
 As x increases, y decreases
 Negative correlation
 Zero
 No change in the y coordinate
 Horizontal line
 Zero divided by any number is zero
 Undefined
 No change in the x-coordinate
 Vertical line
 Any number divided by zero is undefined!
More on Slope!!
 A positive slope… going
up!
 A negative slope….skiing
down!
A horizontal line…. Cross
country skiing….hard
work!
vertical line…falling!
Forms of Linear Equations
 Standard Form

Ax + By = C
 Solve for y

y = ??x + ?? Will learn more later
 y - y₁ = m( x - x₁)
Where did that come from????
recall
m = (y₂- y₁)
( x₂ - x₁)
Examples with point slope form
and standard form
 Write an equation in point slope form for (show line)
 A line that passes through (-3, 5) and has slope of -




3/4
A line that passes through (0, 5) and has slope of 3
A horizontal line passing though (-6,2)
Write y +5 = -5/4(x-2) in standard form
Write and equation in point slope form and standard
form for a line with points (-8,3) and (4,5)
Slope-Intercept Form
 Y = mx + b
 Look familiar???
 m = slope
 b = y- intercept
 Easiest form to use when graphing
 *** all three forms: standard, point-slope, and slope
intercept are useful in different situations
Families of linear equations
Change sign of slope
Change steepness of slope
Change y-intercept
Parallel and Perpendicular Lines
• Parallel lines have

The same slope
 Non-parallel or intersecting have
 different slopes
 Perpendicular lines have
 opposite reciprocals as their slopes
One more formula…
 Mid point of a line in the coordinate plane