Without graphing, identify the slope and \( y \)-intercept of the line represented by each equation below. Homework Help \( \begin{array}{ll}\text { a. } y=3 x+5 & \text { b. } y=\frac{5}{-4} x \\ \text { c. } y=3 & \text { d. } y=7+4 x\end{array} \)

To identify the slope and \( y \)-intercept of each equation, we can compare them to the slope-intercept form of a line, which is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the \( y \)-intercept. Let's analyze each equation: **a.** \( y = 3x + 5 \) - Slope (\( m \)): 3 - \( y \)-intercept (\( b \)): 5 **b.** \( y = \frac{5}{-4}x \) - Slope (\( m \)): \( \frac{5}{-4} = -\frac{5}{4} \) - \( y \)-intercept (\( b \)): 0 (since there is no constant term) **c.** \( y = 3 \) - Slope (\( m \)): 0 (this is a horizontal line) - \( y \)-intercept (\( b \)): 3 (the line crosses the \( y \)-axis at 3) **d.** \( y = 7 + 4x \) We can rewrite this in slope-intercept form: \[ y = 4x + 7 \] - Slope (\( m \)): 4 - \( y \)-intercept (\( b \)): 7 In summary: - **a.** Slope: 3, \( y \)-intercept: 5 - **b.** Slope: \(-\frac{5}{4}\), \( y \)-intercept: 0 - **c.** Slope: 0, \( y \)-intercept: 3 - **d.** Slope: 4, \( y \)-intercept: 7