13. Graph \( y=-x \) and the point \( (4,-5) \). Is the point on the line?

To determine whether the point \( (4, -5) \) lies on the line defined by the equation \( y = -x \), follow these steps: 1. **Substitute the x-coordinate of the point into the equation:** \[ y = -x \\ y = -4 \] 2. **Compare the result with the y-coordinate of the point:** The calculated y-value is \( -4 \), but the y-coordinate of the point is \( -5 \). \[ -4 \neq -5 \] Since \( -4 \) does not equal \( -5 \), the point \( (4, -5) \) **does not** lie on the line \( y = -x \). --- ### Visual Representation If we were to graph the line \( y = -x \) and plot the point \( (4, -5) \), it would look like this: - **Line \( y = -x \):** This is a straight line that passes through the origin \( (0, 0) \) with a slope of \( -1 \). For every unit increase in \( x \), \( y \) decreases by 1. - **Point \( (4, -5) \):** Located at 4 units to the right of the origin and 5 units below the x-axis. Since the point \( (4, -5) \) does not satisfy the equation \( y = -x \), it will appear **below** the line when graphed. --- ### Summary - **Equation of the line:** \( y = -x \) - **Given point:** \( (4, -5) \) - **Verification:** Substitute \( x = 4 \) into the equation to get \( y = -4 \). Since \( -4 \neq -5 \), the point is not on the line. **Conclusion:** The point \( (4, -5) \) is **not** on the line \( y = -x \).