What is the slope of the line represented by the equation y = 2x + 3?

What is the slope of the line represented by the equation y = 2x + 3?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (B)

The slope of a line in the slope-intercept form of a linear equation can be identified directly from the equation \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept. In this case, the equation given is \(y = 2x + 3\). Here, the coefficient of \(x\) is 2, which indicates that the slope of the line is 2. This means that for every 1 unit increase in \(x\), \(y\) increases by 2 units. This positive slope indicates that the line rises as it moves from left to right on a graph. Understanding that slope is a measure of steepness allows you to visualize how quickly the line ascends or descends. A slope of 2 indicates a relatively steep incline compared to other values, which are less than 2. Thus, the correct identification of the slope from the equation is crucial for analyzing the line's behavior and for interpreting its graph accurately.

The slope of a line in the slope-intercept form of a linear equation can be identified directly from the equation (y = mx + b), where (m) represents the slope and (b) represents the y-intercept.

In this case, the equation given is (y = 2x + 3). Here, the coefficient of (x) is 2, which indicates that the slope of the line is 2. This means that for every 1 unit increase in (x), (y) increases by 2 units. This positive slope indicates that the line rises as it moves from left to right on a graph.

Understanding that slope is a measure of steepness allows you to visualize how quickly the line ascends or descends. A slope of 2 indicates a relatively steep incline compared to other values, which are less than 2. Thus, the correct identification of the slope from the equation is crucial for analyzing the line's behavior and for interpreting its graph accurately.