sat suite question viewer
Algebra
/ Linear equations in two variables
Difficulty: Hard
| 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 
?
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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.