Bell Assignment

Find the slope of the line between the two points. 1. (-1,2) and (2,2) 2. (0,4) and (1, -1) 3. (3,4) and (3,1) Remember the slope formula:

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.

y = -3x + 3

3x + y – 3 = 0

Example 3: Find the slope and y-intercept of the following equations.

• (a) x + 2y = 2 m = ___________ b = __________

• (b) y = 2 m = ___________ b = __________

• (c) x = -5 m = ___________ 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.

(b)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

3. Write an equation of the line that passes through (-3,5) and is perpendicular to the line y = 3x – 4