| x | \n\t\t\t\t||||
| f(x) | \n\t\t\t\t21 | \n\t\t\t\t18 | \n\t\t\t\t15 | \n\t\t\t\t12 | \n\t\t\t
\n
| x | \n\t\t\t\t||||
| f(x) | \n\t\t\t\t21 | \n\t\t\t\t18 | \n\t\t\t\t15 | \n\t\t\t\t12 | \n\t\t\t
\n
The table above shows some values of x and their corresponding values for the linear function f. What is the x-intercept of the graph of
in the xy-plane?
Choice B is correct. The equation of a linear function can be written in the form , where
, m is the slope of the graph of
, and b is the y-coordinate of the y-intercept of the graph. The value of m can be found using the slope formula,
. According to the table, the points
and
lie on the graph of
. Using these two points in the slope formula yields
, or
. Substituting
for m in the slope-intercept form of the equation yields
. The value of b can be found by substituting values from the table and solving; for example, substituting the coordinates of the point
into the equation
gives
, which yields
. This means the function given by the table can be represented by the equation
. The value of the x-intercept of the graph of
can be determined by finding the value of x when
. Substituting
into
yields
, or
. This corresponds to the point
.
Choice A is incorrect and may result from substituting the value of the slope for the x-coordinate of the x-intercept. Choice C is incorrect and may result from a calculation error. Choice D is incorrect and may result from substituting the y-coordinate of the y-intercept for the x-coordinate of the x-intercept.
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