What is the slope of the line represented by the equation y = 3x + 5?

What is the slope of the line represented by the equation y = 3x + 5?

• A. 1
• B. 3
• C. 5
• D. 0

Answer: (B)

The equation given is in the slope-intercept form, which is expressed as \( y = mx + b \). In this format, \( m \) represents the slope of the line, and \( b \) represents the y-intercept. Looking at the equation \( y = 3x + 5 \), we can identify the coefficient of \( x \), which is \( 3 \). This coefficient is the slope of the line. Therefore, the slope of the line is \( 3 \), indicating that for every unit increase in \( x \), \( y \) increases by \( 3 \) units. The y-intercept, represented by \( b \), is \( 5 \) in this case, which tells us where the line crosses the y-axis. The slope provides critical information about the steepness and direction of the line, with a positive value signifying that the line rises as it moves from left to right. Hence, the correct answer reflects the direct association between the coefficient of \( x \) in the equation and the slope of the line.

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

Looking at the equation ( y = 3x + 5 ), we can identify the coefficient of ( x ), which is ( 3 ). This coefficient is the slope of the line. Therefore, the slope of the line is ( 3 ), indicating that for every unit increase in ( x ), ( y ) increases by ( 3 ) units.

The y-intercept, represented by ( b ), is ( 5 ) in this case, which tells us where the line crosses the y-axis. The slope provides critical information about the steepness and direction of the line, with a positive value signifying that the line rises as it moves from left to right. Hence, the correct answer reflects the direct association between the coefficient of ( x ) in the equation and the slope of the line.