Question x-y-3-
| x | y |
| 3 | 7 |
| k | 11 |
| 12 | n |
The table above shows the coordinates of three points on a line in the xy-plane, where k and n are constants. If the slope of the line is 2, what is the value of 
?
x y 3 7 k 11 12 n The table above shows the coordinates of three
Hard-difficulty · SAT Math · Linear Equations in Two Variables — Writing equations from data/points. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
The correct answer is 30. The slope of a line can be found by using the slope formula, 
. It’s given that the slope of the line is 2; therefore, 
. According to the table, the points 
and 
lie on the line. Substituting the coordinates of these points into the equation gives 
. Multiplying both sides of this equation by 
gives 
, or 
. Solving for k gives 
. According to the table, the points and 
also lie on the line. Substituting the coordinates of these points into gives 
. Solving for n gives 
. Therefore, 
, or 30.
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