? Exercise 2.2.1 Consider that the slope \( -\frac{2}{3} \) in Example 2 could also be written as \( \frac{2}{-3} \). Using \( \frac{2}{-3} \) and starting at the vertical intercept, find another point on the graph that has a negative \( x \) value. \( (x, y)=\square \)

To solve this problem, we'll use the information provided about the slope and the vertical intercept. ### Given: - **Slope**: \( \frac{2}{-3} \) (which is equivalent to \( -\frac{2}{3} \)) - **Vertical Intercept**: Let's assume it's at \( (0, b) \) (where \( b \) is the y-coordinate of the intercept). ### Steps to Find Another Point with Negative \( x \)-Value: 1. **Understand the Slope**: - The slope \( \frac{2}{-3} \) indicates that for every 3 units you move horizontally to the left (since the run is negative), the vertical position increases by 2 units. 2. **Starting at the Vertical Intercept**: - Start at \( (0, b) \). 3. **Apply the Slope to Find the Next Point**: - **Horizontal Movement (\( \Delta x \))**: Move **-3** units (to the left). - **Vertical Movement (\( \Delta y \))**: Move **+2** units (upwards). 4. **Calculate the Coordinates of the Next Point**: - **New \( x \)-coordinate**: \( 0 + (-3) = -3 \) - **New \( y \)-coordinate**: \( b + 2 = b + 2 \) 5. **Resulting Point**: - \( (-3, b + 2) \) ### Example with a Specific Vertical Intercept: If, for instance, the vertical intercept is \( (0, 1) \), then: - The next point would be \( (-3, 1 + 2) = (-3, 3) \). ### Final Answer: Assuming the vertical intercept is \( (0, 1) \) (as an example), another point with a negative \( x \)-value is: \[ (x, y) = (-3,\ 3) \] However, without the specific value of the vertical intercept from Example 2, the general form of the answer is: \[ (x, y) = (-3,\ b + 2) \] Where \( b \) is the y-coordinate of the vertical intercept.