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. 0
• B. 1
• C. 2
• D. 3

Answer: (C)

To determine the slope of a line from its equation, it is helpful to recognize the standard form of a linear equation, which is \(y = mx + b\). In this form, \(m\) represents the slope of the line, while \(b\) is the y-intercept. In the equation \(y = 2x + 3\), we can clearly see that it matches the form \(y = mx + b\). Here, \(m\) is equal to 2, which indicates that for every increase of 1 in the \(x\) value, the \(y\) value increases by 2. This positive slope suggests that the line rises as it moves from left to right across the graph. Therefore, the slope of the line is correctly identified as 2. Understanding this concept allows one to quickly determine the slope from similar linear equations by identifying the coefficient of \(x\).

To determine the slope of a line from its equation, it is helpful to recognize the standard form of a linear equation, which is (y = mx + b). In this form, (m) represents the slope of the line, while (b) is the y-intercept.

In the equation (y = 2x + 3), we can clearly see that it matches the form (y = mx + b). Here, (m) is equal to 2, which indicates that for every increase of 1 in the (x) value, the (y) value increases by 2. This positive slope suggests that the line rises as it moves from left to right across the graph.

Therefore, the slope of the line is correctly identified as 2. Understanding this concept allows one to quickly determine the slope from similar linear equations by identifying the coefficient of (x).