Question

Suppose a function can be written in y = mx + b form. What must be true about its graph? Select all that apply.

A. The line rises from left to right.

B. Its graph is a line that crosses the y-axis.

C. Its graph must go through the origin.

D. Its graph crosses the x-axis

E. Its graph is a line that is not vertical

Answer 1

For a function that can be expressed in the form \( y = mx + b \), the following statements are true:

**B. Its graph is a line that crosses the y-axis.**
- The \( y \)-intercept \( b \) in the equation represents the point where the line crosses the y-axis.

**E. Its graph is a line that is not vertical.**
- The equation \( y = mx + b \) represents a linear function where \( m \) is the slope. Since slopes for vertical lines are undefined, a function in this form cannot represent a vertical line.

The other options are not necessarily true:

**A. The line rises from left to right.**
- This is true only if the slope \( m \) is positive. If \( m \) is negative, the line will fall from left to right.

**C. Its graph must go through the origin.**
- This is only true if \( b = 0 \). Otherwise, the line will not pass through the origin.

**D. Its graph crosses the x-axis.**
- This is true only if the equation has a solution for when \( y = 0 \), which may not happen if the line is entirely above or below the x-axis depending on the values of \( m \) and \( b \).

Thus, the correct statements are **B** and **E**.