What does it mean to say that a function is linear? Select all that apply. \( \square \) A. The function has a graph that includes the point \( (0,0) \). \( \square \) B. The function can be described by an equation of the form \( \mathrm{y}=\mathrm{mx}+\mathrm{b} \). \( \square \) C. The function has a constant rate of change. \( \square \) D. The function has a rate of change that increases. \( \square \) E. The function has a straight-line graph.

To determine what it means for a function to be linear, let's analyze each option: - **A. The function has a graph that includes the point \( (0,0) \).** - This is true for linear functions that pass through the origin, but not all linear functions must pass through this point. Therefore, this statement is not universally true for all linear functions. - **B. The function can be described by an equation of the form \( \mathrm{y}=\mathrm{mx}+\mathrm{b} \).** - This is true. A linear function can indeed be expressed in this form, where \( m \) is the slope and \( b \) is the y-intercept. - **C. The function has a constant rate of change.** - This is true. Linear functions have a constant rate of change, which is represented by the slope \( m \) in the equation \( \mathrm{y}=\mathrm{mx}+\mathrm{b} \). - **D. The function has a rate of change that increases.** - This is false. A linear function has a constant rate of change, not one that increases or decreases. - **E. The function has a straight-line graph.** - This is true. The graph of a linear function is always a straight line. Based on this analysis, the correct options that apply to a linear function are: - **B. The function can be described by an equation of the form \( \mathrm{y}=\mathrm{mx}+\mathrm{b} \).** - **C. The function has a constant rate of change.** - **E. The function has a straight-line graph.**