Question

how does the value of b affect the graph of y = mx + b?

• it translates the graph up or down the y-axis by b units.
• it affects the steepness of the graph and determines whether the line rises or falls.
• it translates the graph left or right on the x-axis by b units.

Explanation:

In the linear equation \( y = mx + b \), \( m \) is the slope (affecting steepness and direction), and \( b \) is the y - intercept. The y - intercept is the point where the line crosses the y - axis. When \( b \) changes, the point of intersection with the y - axis changes, which results in a vertical translation (up or down) of the graph. The option about steepness refers to \( m \), and the option about horizontal translation is incorrect for \( b \).

Answer:

A. It translates the graph up or down the \( y \)-axis by \( b \) units.