ID: 0366d965
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: "What's in the box?" (Seven)
Method 1: If the slope of the line is 2, you can find any other point on the line given a single point, and that is just what we have in (3, 7). Since the next point given, (k, 11), has a change in y of 4, it must be true that there is a corresponding change in x of 2 for the slope to be 2 (change in y divided by change in x). Hence, k must be 3 + 2, or 5. To, get n, apply the same process. The gap between k, 5, and 12 is 7, so the gap between 11 and n must be 2 * 7, or 14: 11 + 14 = 25, so n must be 25.
k + n = (5) + (25) = 30
The correct answer is 30.
It might be easier to visualize using the box (or something like it). Notice the gaps the first two rows' y-values. This understanding leads to solving for k, which, in turn, leads to solving for n.
x | y
3 | 7
k | 11
12 | n
Method 2: There is a way to use Desmos other than as a simple calculator, building off of the above method. You could recreate the equation of the line, since you know the slope and a point, (3, 7).
y = mx + b
(7) = (2)(3) + b
7 = 6 + b
1 = b
y = 2x + 1
The graph will clearly show the point (3, 7), from which you can either look for the points in question or create a table, as I have to illustrate. (Click on "Edit List," the gear icon above the equation, then "Create Table.") Finally, do not forget to answer the question.
Method 3: Given any two points on a line, you can calculate the slope. Here, you need to use the point (3, 7) and one of the other two points, as well as the given slope of 2, to solve for one of the unknowns. Then, you can solve for the other. Since (k, 11) is in the second row, it seems more natural for me to start there.
m = (11 - 7)/(k - 3)
(2) = 4/(k - 3)
At this point, you could either multiply both sides by (k - 3) and then solve or just deduce that since 4/2 = 2, it must be true that k - 3 = 2. I prefer the latter approach.
k - 3 = 2
k = 5
You can repeat the process for (12, n).
m = (n - 7)/(12 - 3)
(2) = (n - 7)/9
18 = n - 7
25 = n
The answer to the question, which asks about the sum of k and n, is 5 + 25, or 30.
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