Problem

For $C(h)=25h+40$, evaluate the model at $h=0$ and interpret the $y\text{-}\text{intercept}$ as a point and initial repair cost, distinguishing it from the slope.

Big Picture

What this problem is really about

The vertical intercept is the model’s output at an input of zero, so its meaning comes from the zero-input context. We’ll substitute zero, express the result as a point with units, and interpret the remaining constant as the initial charge. Contrasting that fixed amount with the variable coefficient will separate starting value from later rate of change.

Answer choices

Choose your path.

Preview only

substitution = C(0)=40; point = (0 hours,$40); meaning = cost increases $40/hour; slope distinction = $25 is initial fee

substitution = C(0)=25; point = (0 hours,$25); meaning = $25 initial service fee; slope distinction = $40/hour

substitution = C(0)=40; point = (0 hours,$40); meaning = $40 initial service fee before repair hours; slope distinction = $25/hour is the later increase

substitution = C(40)=0; point = (40 hours,$0); meaning = no cost after 40 hours; slope distinction = $25/hour

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

For \(C(h)=25h+40\), evaluate the model at \(h=0\) and interpret the \(y\text{-}\text{intercept}\) as a point and initial repair cost, distinguishing it from the slope.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.