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.
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