2.  Find the slope-intercept form, given a linear equation  Graph the line described the slope-intercept form  What is the relationship between the slopes of parallel lines?  What is the relationship between the slopes of perpendicular lines?

3.  Recall the point-intercept form of linear equation. y – y 1 ----- = m x – x 1 y – y 1 = m (x – x 1 )  E.g., y – 1 = 3(x – 2)

4. y – y 1 = m(x – x 1 ) Suppose (x 1, y 1 ) = (0, b) Then y – y 1 = m(x – x 1 ) y – b = mx y = mx + b m = slope b = y-intercept

5. y = ½ x + 3 m = ½ b = 3 y = 2 x – 5 m = 2 b = -5

6. Find the slope and the y-intercept of the line. a) 2x + 5y = 3 5y = -2x + 3 y = (-2/5)x + 3/5 m = -2/5 b = 3/5 b) 3x – 4y = 9

7.  Suppose a line has a slope of 5 and passes through (-2, 9). Write the slope-intercept form of the equation for the line.  Solution y = mx + b 9 = 5(-2) + b 19 = b y = 5x + 19

8.  Suppose that a line passes through the following 2 points: (-3, 4), (5, -8). Write the slope-intercept form of the equation of the line.  Solution: m = (-8 – 4)/(5 – (-3)) = -12/8 = -3/2 y = mx + b 4 = (-3/2)(-3) + b 4 = 9/2 + b b = -1/2 y = (-3/2)x – 1/2

9.  y = (4/3)x – 2 m = 4/3 b = -2

10.  Find the slope and the y-intercept of the line: 2(x – 3) = –3(y + 5). Graph the equation.  Solution  2x – 6 = -3y – 15 3y = -2x – 9 y = (-2/3)x – 3 m = -2/3 b = -3

11.  Show that the lines represented by 4x + 8y = 16 and x = 6 – 2y are parallel.  Two lines are parallel if their slopes are equal 4x + 8y = 16 x = 6 – 2y 8y = -4x + 16 2y = -x + 6 y = -(1/2)x = 2 y = (-1/2) + 3

12.  2 and -1/2 are negative reciprocals of each other.  So are 3/4 and -4/3.  What is the negative reciprocal of 3/5?  If two lines are perpendicular to each other, their slopes are negative reciprocals  If the slopes of two lines are negative reciprocals, the lines are perpendicular.

14.  Write an equation of the line passing through (–3, 2) and parallel to the line y = 8x – 5.  Solution: Solve for b, in y = mx + b

15. A company buys a $12,500 computer with an estimated life of 6 years. The computer can then be sold as scrap for an estimated salvage value of $500. If y represents the value of the computer after x years of use and y and x are related by the equation of a line, a. Find an equation of the line and graph it. b. Find the value of the computer after 2 years. c. Find the economic meaning of the y-intercept of the line. d. Find the economic meaning of the slope of the line.