Problema Solution
4. The line
represents an estimate of the average cost of gasoline each year. The line
estimates the price of gasoline in January of each year (“Consumer price index,” 2006).
a. Do you expect the lines to be intersecting, parallel, or perpendicular? Explain your reasoning.
b. Use the equations of the lines to determine if they are parallel. What did you find?
c. Did your answer to Part b. confirm your expectation in Part a?
Answer provided by our tutors
a) The givens of the lines are,
y=0.15x+0.79 ...(1)
and 0.11x-y=-0.85
0.11x+0.85 = y
y=0.11x+0.85 ...(2)
The slope of the first line is = 0.15
The slope of the second line is = 0.11
Since the slopes are not equal, the lines are not parallel. So they will intersect.
b)
Product of the slopes is (0.15)*(0.11) = 0.0165 (not equal to -1)
So the lines are not perpendicular.
(1)-(2)=> 0 = 0.04x-0.06
-0.04x=-0.06
x=(-0.06)/(-0.04)
x=3/2 =1.5
(1) => y = 0.15*1.5+0.79
y = 0.225+0.79
y = 1.015
The point of intersection is (1.5,1.015)
c) Did your answer to part b confirm your expectation in part a? Yes