Sketch the graph of each line. \[ \begin{array}{ll}\text { 1) } y=\frac{1}{4} x-1 & b=-1\end{array} \]

To sketch the graph of the line \( y = \frac{1}{4}x - 1 \), follow these steps: ### 1. Identify the Slope and Y-Intercept - **Slope (m):** \( \frac{1}{4} \) - **Y-Intercept (b):** \( -1 \) ### 2. Plot the Y-Intercept The y-intercept is the point where the line crosses the y-axis. For this equation: - **Point:** \( (0, -1) \) ### 3. Use the Slope to Find Another Point The slope \( \frac{1}{4} \) means that for every increase of 4 units in \( x \) (run), \( y \) increases by 1 unit (rise). Starting from the y-intercept \( (0, -1) \): - **Rise:** 1 unit up - **Run:** 4 units to the right - **Second Point:** \( (4, 0) \) ### 4. Draw the Line - Plot the two points \( (0, -1) \) and \( (4, 0) \) on a coordinate plane. - Use a ruler to draw a straight line passing through these points. - Extend the line in both directions beyond the plotted points. ### 5. Label the Graph - **XAxis:** Label as \( x \) - **YAxis:** Label as \( y \) - **Points:** Mark and label the points \( (0, -1) \) and \( (4, 0) \) - **Line:** Optionally, write the equation \( y = \frac{1}{4}x - 1 \) alongside the line for clarity. ### Visual Representation While I can't provide an actual sketch here, following the steps above will help you visualize the line: 1. Start at \( (0, -1) \) on the y-axis. 2. Move right 4 units and up 1 unit to reach \( (4, 0) \). 3. Draw a straight line through these points extending infinitely in both directions. The line will slope gently upward from left to right, reflecting the positive slope of \( \frac{1}{4} \). --- **Summary:** - **Equation:** \( y = \frac{1}{4}x - 1 \) - **Slope:** \( \frac{1}{4} \) (gentle upward slope) - **Y-Intercept:** \( (0, -1) \) - **Another Point:** \( (4, 0) \) - **Graph:** A straight line passing through \( (0, -1) \) and \( (4, 0) \), extending infinitely in both directions.