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Advanced Math
/ Nonlinear equations in one variable and systems of equations in two variables
Difficulty: Hard
In the xy-plane, the graph of 
intersects line p at 
and 
, where a and b are constants. What is the slope of line p ?
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Explanation
Choice A is correct. It’s given that the graph of and line p intersect at and . Therefore, the value of y when 
is the value of a, and the value of y when 
is the value of b. Substituting 1 for x in the given equation yields 
, or 
. Similarly, substituting 5 for x in the given equation yields 
, or 
. Therefore, the intersection points are 
and 
. The slope of line p is the ratio of the change in y to the change in x between these two points: 
, or 6.
Choices B, C, and D are incorrect and may result from conceptual or calculation errors in determining the values of a, b, or the slope of line p.