Transcript Lesson 1.1 Notes

Bell Assignment
Find the slope of the line between the two points.
1. (-1,2) and (2,2)
2. (0,4) and (1, -1)
Remember the slope formula:
3. (3,4) and (3,1)
m = y2 – y1
x2 – x1
1.1 Lines in the Plane
A graph is a ____________________________
• Solutions are _______________
___________________________.
Consider the equation: x + y = 5
Find 4 solutions to the equation
and plot the points.
3 Important Forms of Linear Equations:
• point - slope form: y – y1 = m(x – x1)
• slope - intercept form: y = mx + b
• general form: Ax + By + C = 0
Other Important Forms
• Vertical Line: x = c (c is a constant)
• Horizontal Line: y = c (c is a constant)
Example 1: Write the equation of a line that passes
through the point (1,-2) and has a slope of 3. Put
answer in general form.
Example 2: Write the equation of the line that goes
through the points (-1,6) and (2,-3). Put it in (a)
slope-intercept form and (b) general form.
3x + y – 3 = 0
y = -3x + 3
Example 3: Find the slope and y-intercept of the
following equations.
• (a) x + 2y = 2
• (b) y = 2
• (c) x = -5
m = ___________
m = ___________
m = ___________
b = __________
b = __________
b = __________
Example 4: Determine the x and y intercepts of the
following equations.
• 2x – y = 6 x-intercept: __________ y –intercept:
__________
• 4x + 2y = 16 x-intercept: __________ y –intercept:
__________
• 5x + y = 15 x –intercept: _________ y –intercept:
__________
Parallel and Perpendicular Lines
• What is the relationship between the slopes of two lines that
are parallel?
• What is the relationship between the slopes of two lines that
are perpendicular?
Example 5: Given the equation 2x – 3y = 5, find an
equation that is (a) parallel and (b) perpendicular
going through the point (2, -1)
Parallel Line
Perpendicular Line
Example 6: Find the slope intercept form of the
equation of the line that passes through the point (4,1) and is parallel to the line 5x – 3y = 8
Example 7: Write the equation of the line that goes
through the point (4, -10) and is perpendicular to
the line 4x – 7y = 12.
Example 8: During 1997, Barnes and Nobles net
sales were $2.8 billion and in 1998 net sales were
$3.0 billion. (Source: Barnes and Nobles, Inc.)
(a)Write a linear equation giving the net sales, y, in terms of the
year, x.
Example 8: During 1997, Barnes and Nobles net
sales were $2.8 billion and in 1998 net sales were
$3.0 billion. (Source: Barnes and Nobles, Inc.)
(b)Use the equation to estimate the net sales during 2000.
Example 9: The net sales for a car manufacturer
were $14.61 billion in 2005 and $15.78 billion in
2006.
(a)Write a linear equation giving the net sales y in terms of x,
where x is the number of years since 2000.
(a)Use the equation to predict the net sales for 2007.
Exit Pass
1. Write an equation of the line that passes through the points (2,1) and (3,2).
2. Write an equation of the line that passes through (-1,1) and is
parallel to the line y = -2x + 1
1. Write an equation of the line that passes through (-3,5) and is
perpendicular to the line y = 3x – 4