can anyone walk me through this problem
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?
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For Part A, it seems reasonable to expect the lines to be approximately parallel. If the average gas price is increasing linearly from year to year, the January gas price would most likely increase in a similar linear fashion. The January price might be lower than the yearly average each year, but we wouldn't expect the rate of growth of the January price from year to year to be any greater than the rate of growth of the average yearly price from year to year.
For Part B, convert the January line to slope-intercept form. You will obtain an equation of the form y=0.11x+0.85. This line has a lower slope than the yearly line of y=0.15x+0.79, so the lines aren't parallel.
For Part C, we can say that the findings confirmed our expectations to a decent extent. We expected the lines to be "approximately" parallel, which they are (the slopes are only 0.04 apart). It's a little bit surprising that the slopes don't match up even more, but the entire gas-price system is complex. We weren't given information concerning the span of the data (5 years? 10 years? 50 years?), and we don't know too much about how gas-prices are set on a global scale, so we shouldn't be too disappointed.
Hope that helps!