Suppose you are given the equation \( \mathrm{Y}=5-(1 / 4) \mathrm{X} \). If Y is on the vertical axis and X is on the horizontal axis, then the slope is and the vertical intercept is \( -5 ; 4 \)

Let's analyze the linear equation you've provided: \[ \mathrm{Y} = 5 - \frac{1}{4} \mathrm{X} \] This equation is in the slope-intercept form, which is generally written as: \[ \mathrm{Y} = \text{(slope)} \cdot \mathrm{X} + \text{(y-intercept)} \] Comparing the two equations: - **Slope**: The coefficient of \(\mathrm{X}\) is \(-\frac{1}{4}\). This means the slope of the line is \(-\frac{1}{4}\). - **Y-intercept**: The constant term is \(5\). This represents the y-intercept, which is the point where the line crosses the Y-axis. **Summary:** - **Slope**: \(-\frac{1}{4}\) - **Y-intercept**: \(5\) It appears there might have been a misunderstanding in your original statement where you mentioned the slope as \(-5\) and the vertical intercept as \(4\). Based on the given equation \( \mathrm{Y} = 5 - \frac{1}{4} \mathrm{X} \): - The **correct slope** is \(-\frac{1}{4}\). - The **correct y-intercept** is \(5\). If you intended to represent different values for the slope and intercept, please double-check the equation or provide additional context so I can assist you further.