What is the slope of the line represented by the equation \( y = 3x + 4 \)?

What is the slope of the line represented by the equation \( y = 3x + 4 \)?

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (B)

The equation given, \( y = 3x + 4 \), is in slope-intercept form, which is expressed as \( y = mx + b \). In this form, \( m \) represents the slope of the line, and \( b \) represents the y-intercept. From the equation, it is clear that the coefficient of \( x \) is 3. This means that the slope of the line is 3. The slope indicates how much \( y \) changes for a unit change in \( x \). In this case, for every 1 unit increase in \( x \), \( y \) increases by 3 units. This understanding of slope as a ratio of change in \( y \) to change in \( x \) is fundamental in graphing linear equations and understanding their behavior. The slope provides insight into the steepness and direction of the line, confirming that the correct answer, representing the slope, is indeed 3.

The equation given, ( y = 3x + 4 ), is in slope-intercept form, which is expressed as ( y = mx + b ). In this form, ( m ) represents the slope of the line, and ( b ) represents the y-intercept.

From the equation, it is clear that the coefficient of ( x ) is 3. This means that the slope of the line is 3. The slope indicates how much ( y ) changes for a unit change in ( x ). In this case, for every 1 unit increase in ( x ), ( y ) increases by 3 units.

This understanding of slope as a ratio of change in ( y ) to change in ( x ) is fundamental in graphing linear equations and understanding their behavior. The slope provides insight into the steepness and direction of the line, confirming that the correct answer, representing the slope, is indeed 3.