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.
complete
how does the value of m affect the graph of
y = mx + b?
○ it translates the graph up or down the y - axis.
○ 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.
done ✓

Explanation:

For the question "How does the value of \( m \) affect the graph of \( y = mx + b \)":

• Recall the slope - intercept form of a linear equation \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.
• The slope \( m \) determines the steepness of the line. If \( m>0 \), the line rises from left to right; if \( m < 0 \), the line falls from left to right. A larger absolute value of \( m \) makes the line steeper.
• The option "It translates the graph up or down the \( y \) - axis" is the effect of \( b \), not \( m \). The option "It translates the graph left or right on the \( x \) - axis" is not the effect of \( m \) on the graph of a linear function in slope - intercept form.

Answer:

B. It affects the steepness of the graph and determines whether the line rises or falls. (Here we assume the options are labeled as follows: A. It translates the graph up or down the \( y \) - axis. B. It affects the steepness of the graph and determines whether the line rises or falls. C. It translates the graph left or right on the \( x \) - axis.)