Answer: The correct option is (C) \(y=4x-13.\)
Step-by-step explanation: We are given to write a rule for the linear function given in the graph.
Since the graph is a straight line, so we are to find the equation of the line to find the rule.
From the graph, we note that
the points (3, -1) and (4, 3) lie on the straight line.
So, the slope of the line will be
\(m=\dfrac{3-(-1)}{4-3}\\\\\\\Rightarrow m=4.\)
Since the line passes through the point (4, 3), so the equation of the line is given by
\(y-3=m(x-4)\\\\\Rightarrow y-3=4(x-4)\\\\\Rightarrow y=4x-16+3\\\\\Rightarrow y=4x-13.\)
Thus, the required rule for the linear function is
\(y=4x-13.\)
Option (C) is correct.
