4. 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?
Put both in the form of y=mx+b
If m's are the same, they are parallel.
a. To determine if the lines are intersecting, parallel, or perpendicular, we need to compare the slopes of the two lines. In the equation y = mx + b, where m is the slope, we can see that the first line has a slope of 0.15, and the second line can be rearranged into the form y = mx + b as well. The coefficient of x in the second equation (0.11x - y = 0.85) is the negative of the slope, so the slope of the second line is -0.11.
If two lines have the same slope, they are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular.
b. To determine if the lines are parallel, we compare the slopes. The slope of the first line is 0.15, and the slope of the second line is -0.11. Since these slopes are not the same, the lines are not parallel.
c. No, my answer to part b. does not confirm my expectation in part a. I initially expected the lines to be parallel or perpendicular, but they are neither. They intersect at some point.