he slope of a line is
and can be calculated using the coordinates of any two points on the line. For example, the graph of
f passes through the points
(0,3) and
(2,4), so the slope of the graph of
f is
= . The slope of the graph of function
g is
4 times the slope of the graph of f, so the slope of the graph of
g is
4()=2 . Since the point
(0,−4) is the y-intercept of g, g is defined as
g(x)=2x−4. It follows that
g(9)=2(9)−4=14.Choice A is incorrect because if g(9) = 5, then the slope of the graph of function g is
=1,which is not 4 times the slope of the graph of f. Choices B and D are also incorrect. The same procedures used to test choice A yields
= and
= for the slope of the graph of
g for choices B and D, respectively. Neither of these slopes is 4 times the slope of the graph of
f