The graph of
y=f(n) in the coordinate plane is a line that passes through each of the points given in the table.
From the table, one can see that an increase of 1 unit in n results in an increase of 3 units in f(n);
for example,
f(2)−f(1)=1−(−2)=3.
Therefore, the graph of
y=f(n) in the coordinate plane is a line with slope 3.
Only choice C is a line with slope 3.
The y-intercept of the line is the value of f(0).
Since an increase of 1 unit in n results in an increase of 3 units in f(n),
it follows that
f(1)−f(0)=3. Since
f(1)=−2, it follows that
f(0)=f(1)−03=−5. Therefore, the y-intercept of the graph of f(n) is −5, and the slope-intercept equation for f(n) is
f(n)=3n−5.Choices A, B, and D are incorrect because each equation has the incorrect slope of the line (the y-intercept in each equation is also incorrect).