If (R(x)=82+mx) and (R(10)-R(4)=72), what is (R(0))?

Correct answer: (82)

For the function \(R(x)=82+mx\), the value at zero is determined by the constant term. Substituting \(x=0\) removes the variable part, since \(m\times0=0\). Therefore \(R(0)\) can be found without first solving for \(m\). The difference condition gives useful information about the slope, but it does not alter the constant value at zero.

Substitution gives \(R(0)=82+m(0)=82\), so option C is correct. The supplied condition is consistent: \(R(10)-R(4)=(82+10m)-(82+4m)=6m=72\), hence \(m=12\). This confirms the rate of change. However, 12 is the slope and 72 is the stated difference; neither is the value of \(R(0)\).