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Linear functions SAT question
Math · Algebra · Easy · Answer it here, explanation included.
The graph of the function f is a line in the xy-plane. If the line has slope 
and 
, which of the following defines f?
ExplanationShow
Choice B is correct. The equation for the function f in the xy-plane can be represented by 
, where m is the slope and b is the y-coordinate of the y-intercept. Since it’s given that the line has a slope of , it follows that 
in , which yields 
. It’s given that . This implies that the graph of the function f in the xy-plane passes through the point 
. Thus, the y-coordinate of the y-intercept of the graph is 3, so 
in 
, which yields 
. Therefore, the equation defines the function f.
Choice A is incorrect and may result from a sign error for the y-intercept. Choice C is incorrect and may result from using the denominator of the given slope as m in , in addition to a sign error for the y-intercept. Choice D is incorrect and may result from using the denominator of the given slope as m in .
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