The box-and-whisker plots show the distribution of quiz scores for two students for a semester. Compare Raul and Homer’s quiz sc
ores from the data provided.
Group of answer choices
Raul had the greater median, and Raul was more consistent in his scores.
Raul had the greater median, and Homer was more consistent in his scores.
Homer had the greater median, and Raul was more consistent in his scores.
Homer had the greater median, and Homer was more consistent in his scores.
Group of answer choices
Raul had the greater median, and Raul was more consistent in his scores.
Raul had the greater median, and Homer was more consistent in his scores.
Homer had the greater median, and Raul was more consistent in his scores.
Homer had the greater median, and Homer was more consistent in his scores.
1 answer:
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2 Answers:
- B) The lines are parallel
- C) The lines have the same slope.
Parallel lines always have equal slope, but different y intercepts.
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Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
