Tip #32 to Get a Top ACT Math Score (page 2)
The graph of the equation y = mx + b is a line. In the equation, m is the slope, sometimes called the rate of change, and b is the y intercept (the place where the line crosses the y axis). Usually, that is enough to get a question right.
Let's take a look at this question:
Solution: The fee for each bottle, $20, goes next to x. And $25 is a fixed fee, unrelated to how many bottles someone buys, so $25 stands alone: y = 20x + 25.
Correct answer: J.
That was so easy to explain that I have some room left. So, here's Brian's Math Magic Trick #2.
y = mx + b Drills
- If a movie trailer offends 45 people in a theater, and then the feature movie disturbs 25 more people every scene the villain appears in, which of the following equations expresses the number of people offended or disturbed after x villain scenes in the movie?
- y = 45
- y = 25x + 45
- y = 20x
- y = 70x
- y = 20x + 70
- Which of the following equations best fits the information in the table below?
- y = 5x – 2
- y = –9.5
- y = 2x – 4
- y = 0.25x + 3
- y = –9.1x
- Which of the following equations could represent the graph in the standard (x, y) coordinate plane shown below?
- y = 2
- y = 2x + 2
- y = 4x
- y = –x + 2
- y = 4x + 4
- If the cost of advertising on Facebook consists of a fixed charge plus a charge per insertion of the ad, based on the table below, what is the fixed charge?
- For the first 10 seconds after a geyser erupts, its height is given by h = 3.4s, where h is in feet and s represents seconds after erupting. When will the geyser first be over 20 feet tall?
- Between 3 and 4 seconds
- Between 4 and 5 seconds
- Between 5 and 6 seconds
- Between 6 and 7 seconds
- Between 7 and 8 seconds
Answer to Brian's Math Magic Trick #2: come on, you should know that there are no elephants in Denmark! To find out how this stunning act of magic works, go to my website: www.BrianLeaf.com/Elephants
- B 25 people are disturbed by each scene, so that number goes next to the x. 45 people were offended right off the bat by the trailer, and this number does not change with the number of disturbing scenes in the movie, so that number goes alone. y = 25x + 45.
- J "Use the Answers"! Just choose an (x, y) pair from the table, such as (8, 5), and test each answer. If two choices work, choose another (x, y) pair and do a tiebreaker. Choice J works since 5 = 0.25(8) + 3.
- B The graph shown crosses the y axis at 2, so it has a "y intercept" of 2, meaning b = 2. The slope is positive because the line rises from left to right, so m > 0. (Review slope in Skill 13 if needed. If you slacked during the slope chapter and did not do the drills, e-mail me and I'll send a motivational speech your way.) Choice B is the only choice that satisfies both requirements: y intercept of 2 and positive slope.
- K The ACT loves y = mx + b, and they are obsessed with fixed costs, which are always the b. Here, we need to add more rows to the table until we get 0 inserts. At zero inserts, the only cost will be the fixed charge, since we won't be paying for any inserts. If we add a row above the current data, for a cost of 33, we have 0 inserts, so the fixed cost is 33.
- C Plug 20 in for h, which represents height. So 20 = 3.4s, and dividing by 3.4, we get 5.88 = s, which is between 5 and 6 seconds.
Go to: Tip #33
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