The line y=0.15x+0.79

represents an estimate of the average cost of gasoline each year.

The line 0.11x-y=-0.85

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?

the first equation has a slope of .15

the 2nd equation has a slope of .11

mmmhhh?

a.The lines are expected to be intersecting ; if not , there would

be no solution to the set of equations.

b. Slope1= 0.15, Slope2=-A/B=-0.11/-1
=0.11. The lines are intersecting,
because the slopes are not equal.

c. Yes.

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a. To determine if the lines are intersecting, parallel, or perpendicular, we need to compare their slopes. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope of the line.

In the first equation, y = 0.15x + 0.79, the slope is 0.15.
In the second equation, we need to rearrange it in slope-intercept form: 0.11x - y = -0.85
By solving for y, we get y = 0.11x + 0.85, which means the slope is 0.11.

b. Since the slopes of the two lines are different (0.15 and 0.11), we can conclude that they are not parallel. To confirm this, we can check if their slopes are reciprocals of each other (perpendicular lines have slopes that are negative reciprocals).

c. The lines being non-parallel supports our initial expectation. Since the slopes are different, they will not be parallel. Therefore, our answer confirms our expectation from Part a.