### 1.4 Equations of Lines and Linear Models

```1.4 Equations of Lines and
Linear Models
Quiz

If two distinct lines, y=m1x+b1, y=m2x+b2 ,
are parallel with each other, what’s the
relationship between m1 and m2?
Point-Slope Form
Given the slope m of a linear function and a
point (x1,y1) on the graph of the linear
function. We write the equation of the
linear function as
y-y1=m(x-x1)
We call a linear equation in this form as
point-slope form of a linear function.
Standard Form
A linear equation written in the form
Ax+By=C, where A,B, and C are real
numbers(A and B not both 0), is said to
be in standard form.
Notice:When A≠0, B=0, the linear equation will
be Ax=C, which is a vertical line and is not a
linear function.
Point-Slope Form
Exercise:
Write the equation of the line through
(-1,3) and (-2,-3).
Does it matter which point is used?
Parallel and Perpendicular Lines
Parallel Lines: Two distinct non-vertical
lines are parallel if and only if they have
the same slope.
y
y=m2x+b2
y=m1x+b1
x
m1=m2
Parallel and Perpendicular Lines
Perpendicular Lines: Two lines, neither
of which is vertical, are perpendicular if
and only if their slopes have product -1
y=m2x+b2
y
y=m1x+b1
x
m1 × m2=-1
Parallel and Perpendicular Lines
Exercises:
1, Write the equation of the line through (-4,5)
that is parallel to y=(1/2)x+4
2, Write the equation of the line through (5,-1)
that is perpendicular to 3x-y=8. Graph both
lines by hand and by using the GC.
3, Write the equation of the line through (2/3,3/4) that is perpendicular to y=1. Graph
both lines by hand and by using the GC.
Linear Applications
Example 1:
The cellular Connection charges \$60 for
a phone and \$29 per month under its
economy plan, Write an equation that can
model the total cost, C, of operating a
Cellular Connection phone for t months.
Find the total cost for six months.
Linear Application
Example 2:
The number of land-line phones in the
US has decreased from 101 million in
2001 to 172 million in 2006. What is the
average rate of change for the number of
land-line phones over that time? Predict
how many land-line phones are in use in
2010.
Linear Regression
Why Linear Regression?
In most real-life situations data seldom
fall into a precise line. Because of
measurement errors or other random
factors, a scatter plot of real-world data
may appear to lie more or less on a line,
but not exactly. Fitting lines to data is one
of the most important tools available to
researchers who need to analyze
numerical data.
Linear Regression
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Linear Regression
Example 1: US infant mortality
Year
Rate
1950
29.2
1960
26.0
1970
20.0
1980
12.6
1990
9.2
2000
6.9
1, Find the regression line for the
infant mortality data.
2, Estimate the infant mortality rate
in 1995.
3, Predict mortality rate in 2006.
Homework

PG. 42: 5-60(M5); 61, 63, 65,
Supplement(linear Regression)

KEY: 20, 45, 50, 63, S: 3, 5
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