Question

During the period 1990 – 2004 the average commute to work in the Greater Washington, D.C. area increased from 20 minutes in 1990 (t = 0) by an average of 3 minutes per year. Use these data to express y, the average number of minutes commuting to work, as a linear function of x, the number of years since 1990.

   3. Find the equation of each line. Put into slope-intercept form whenever possible.

   (a) The vertical line through (0,0).

   (b) The line parallel to the line x − 4y = 12 and passing through (8,1).

(c) The line through (5, −7) and decreasing at a rate of 3 units of y per 5 units of x.

(d) The horizontal line through (3,6).

(e) The line through (-8,12) that is perpendicular to the line given by 3x + 4y = 27.

Answer 1

1) slope = 3 minutes per year

Greater Washington, D.C. area increased from 20 minutes

hence, equation can be written as

y = 3x + 20

3)a) vertical line through (0,0)

x = 0

b) parallel to x - 4y = 12 and passing through (8,1)

slope of parallel lines are same

slope is

4y = x - 12

y = 1/4 x - 3

slope = 1/4

y - 1 = 1/4 ( x - 8 )

y = 1/4x -1

c) line through ( 5, - 7)

slope = -3/5

y + 7 = - 3/5 ( x - 5)

y = - 3/5 x - 4

d) horizontal line through ( 3, 6 )

y = 6

e)  perpendicular to 3x + 4y = 27

slopes of perpendicular lines are negative reciprocal of each other

4y = - 3x + 27

y = -3/4 x + 27/4

slope of perpendicular line is 4/3

y - 12 = 4/3 ( x + 8 )

y = 4/3 x + 68/3