2. Without using a graphing calculator, identify all of the following equations that straight lines. Explain how you decide. \( \begin{array}{ll}\text { a. } y=3 x & \text { e. } y=\frac{1}{x}+3\end{array} \)

To determine which of the given equations represent straight lines, we need to analyze their forms. A straight line can be represented in the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Let's examine each equation: ### a. \( y = 3x \) This equation is already in the slope-intercept form: - Here, \( m = 3 \) (the slope) and \( b = 0 \) (the y-intercept). - Since it can be expressed as \( y = mx + b \), this equation represents a straight line. ### e. \( y = \frac{1}{x} + 3 \) This equation is not in the slope-intercept form. To analyze it further: - The term \( \frac{1}{x} \) indicates that this equation is not linear. Instead, it represents a hyperbola, as it involves a variable in the denominator. - The presence of \( \frac{1}{x} \) means that as \( x \) approaches zero, \( y \) approaches infinity, and as \( x \) increases or decreases, \( y \) will not change linearly. ### Conclusion - **Equation a** \( y = 3x \) is a straight line. - **Equation e** \( y = \frac{1}{x} + 3 \) is not a straight line. Thus, the only equation that represents a straight line is **a. \( y = 3x \)**.