SAT Mathematics Practice Test 3

The graph of $\mathit{y}=\mathit{f}\left(\mathit{n}\right)$ 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,$\mathit{f}\left(2\right)-\mathit{f}\left(1\right)=1-\left(-2\right)=3$.
Therefore, the graph of $\mathit{y}=\mathit{f}\left(\mathit{n}\right)$ 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 $\mathit{f}\left(1\right)-\mathit{f}\left(0\right)=3.$ Since $\mathit{f}\left(1\right)=-2$, it follows that $\mathit{f}\left(0\right)=\mathit{f}\left(1\right)-03=-5.$
Therefore, the y-intercept of the graph of f(n) is −5, and the slope-intercept equation for f(n) is $\mathit{f}\left(\mathit{n}\right)=3\mathit{n}-5.$
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).