Which of the following equations represents a straight line?

Which of the following equations represents a straight line?

• A. y = x² + 3
• B. y = mx + b
• C. y = 1/x
• D. x² + y² = r²

Answer: (B)

The equation that represents a straight line is of the form \( y = mx + b \), where \( m \) represents the slope of the line and \( b \) represents the y-intercept. This equation is linear because it defines a relationship between \( x \) and \( y \) where the power of both variables is one, resulting in a constant rate of change. In contrast, the other options define different types of relationships: - The equation \( y = x² + 3 \) describes a parabola, which is a curve rather than a straight line, as it includes a squared term. - The equation \( y = 1/x \) represents a hyperbola, characterized by the inverse relationship between \( x \) and \( y \), leading to a non-linear graph. - The equation \( x² + y² = r² \) represents a circle, another non-linear graph, where every point (x, y) that satisfies the equation lies on the circumference defined by the radius \( r \). Thus, among the listed options, only the equation \( y = mx + b \) distinctly represents a straight line.

The equation that represents a straight line is of the form ( y = mx + b ), where ( m ) represents the slope of the line and ( b ) represents the y-intercept. This equation is linear because it defines a relationship between ( x ) and ( y ) where the power of both variables is one, resulting in a constant rate of change.

In contrast, the other options define different types of relationships:

• The equation ( y = x² + 3 ) describes a parabola, which is a curve rather than a straight line, as it includes a squared term.

• The equation ( y = 1/x ) represents a hyperbola, characterized by the inverse relationship between ( x ) and ( y ), leading to a non-linear graph.

• The equation ( x² + y² = r² ) represents a circle, another non-linear graph, where every point (x, y) that satisfies the equation lies on the circumference defined by the radius ( r ).

Thus, among the listed options, only the equation ( y = mx + b ) distinctly represents a straight line.