Transcript 2 – 4 Writing Expressions of Lines Day 1

2 – 4: Writing Expressions
of Lines (Day 1 )
Objective:
CA Standard 1: Students solve equations and
inequalities involving absolute value.
Writing Linear Equations
Slope - Intercept Form: Given the slope m
and the y-intercept b, use this equation
y  mx  b
Point – Slope Form: Given the slope m and a
point (x1, y1), use this equation:
y  y1  m  x  x1 
Two Points: Given two point (x1, y1), and (x2,
y2), use the formula
y2  y1
m
x2  x1
to find the slope m.
Example 1: Writing an Equation Given the slope
and y-intercept.
4
2
3
-5
5
(0,-1)
2
-2
From the graph of the line determine the
slope.
m = 3/2
What is the y-intercept?
(0, -1)
What is an equation of this line?
y = mx +b
y = 3/2 x – 1
Example 2
Write an equation of the line that passes
through (2, 3) and has a slope of – ½ .
Use the point – slope form
y  y1  m  x  x1 
x
y  3   1
2
1
y  3    x  2
2
x
y  4
2
Example 3
Write an equation of a line that passes
through (3, 2) and is parallel to the line
y = -3x +2.
If two lines are parallel they have the
same slope.
Let m = -3 and (x1, y1) = (3, -2)
Use the point slope form.
y  2  3  x  3
y  2  3  x  3
y  2  3 x  9
y  3 x  11
Example 4
Write an equation of a line that passes
through (3, 2) and is perpendicular to the line
y = -3x +2.
If two lines are perpendicular then the
product of their slopes is –1.
Let m1 = -3
m1 m 2 = -1
-3  m2 = - 1
m2 = -1/-3
m2 = 1/3
Use the point slope form
find the equation of the line
y  y1  m  x  x1 
1
y  2   x  3
3
x
y  2  1
3
x
y  1
3
Example 5:
Write an equation of a line that passes
through
(-2, -1) and (3, 4)
Find the slope:
y2  y1 4  1
m

x2  x1 3  2
5
 1
5
Use the point slope form.
y  y1  m  x  x1 
y  1  1 x  2
y 1  x  2
y 1  x  2
Example 6: Writing and using a Linear
Model.
In 1984 Americans purchased an average of
113 meals or snacks per person at
restaurants. By 1996 this number was 131.
Write a linear model for the number of meals
or snacks purchased per person annually.
Then use the model to predict the number of
meals that will be purchased per person in
2006.
Average rate of change
131  113

1996  1984
18 3

  1.5
12 2
Verbal Model:
Labels
Number of Meal
y
Number in 1984
113
Average Rate of change 1.5
Year since 1984
t = 2006 –1984
t = 22
Algebraic Model
y = 113 + 1.5 t
y = 113 + 1.5 (22)
y = 113 + 33
y = 146
Home work
page 95 14 – 42 even, and 61