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 = y 2 – y 1 x 2 – x 1

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 – y 1 = m(x – x 1 ) 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 LinePerpendicular 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 (a)Write a linear equation giving the net sales y in terms of x, where x is the number of years since (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 Write an equation of the line that passes through (-3,5) and is perpendicular to the line y = 3x – 4