SOLUTION: 4. The line y=0.15x + 0.79 represents an estimate of the average cost of gasoline for each year. The line 0.11x-y= -0.85 estimates the price of gasoline in January

Question 239049: 4. The line y=0.15x + 0.79

represents an estimate of the average cost of gasoline for each year. The line
0.11x-y= -0.85
estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 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 by Theo(13342) (Show Source): You can put this solution on YOUR website!
First line is y = .15x + .79
Second line is 0.11x-y= -0.85
Solve for y in the second line to get:
y = .11x + .85
These lines are not parallel or perpendicular because the slopes are not the same or negative reciprocals of each other.

The slope-intercept form of a straight line is y = mx + b where m is the slope.
First line has slope of .15
Second line has slope of .11

These lines will intersect.
Solve these 2 equations simultaneously to find the intersection.

The equations are:
y = .15x + .79
y = .11x + .85

Mulltiply first eqution by 11 and second equation by 15 to get:

11y = 1.65x + 8.69
15y = 1.65x + 12.75

subtract second equation from first to get:

4y = 4.06

divide both sides by 4 to get:

y = 1.015

substitute in first equation original to get:

1.015 = .15x + .79

solve for x to get:

.15x = 1.015 - .79 = .225 which makes x = .225/.15 = 1.5

y = 1.015 and x = 1.5

substitute in second original equation to get:

1.015 = .11x + .85 becomes 1.015 = .11*1.5 + .85 = .165 + .85 = 1.015 which is true.

The two lines intersect at (x,y) = (1.5,1.015)

graph of these two equations is:

horizontal line was put in at y = 1.015 to help you see the intersection point better.

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