If (R(x)=65+mx) and (R(9)-R(4)=55), what is (R(0))?

Correct answer: (65)

In the linear function \(R(x)=65+mx\), the value at \(x=0\) is found directly by substituting zero. The term containing \(m\) disappears because \(m\times0=0\). Thus the constant term is the value where the graph meets the vertical axis. The extra condition involving two function values can be used to find the slope, but it is not needed to find \(R(0)\).

Indeed, \(R(0)=65+m(0)=65\), so option C follows immediately. The given difference also checks consistently: \(R(9)-R(4)=(65+9m)-(65+4m)=5m=55\), giving \(m=11\). This confirms the function but does not change its initial value. A value such as 55 or 11 describes the difference or slope, not \(R(0)\).