- View Image Description A coordinate systern with the followitigy ettributes: - Three points are plotted at \( (-4,5)(4,1) \), and \( (8,-1) \) - A straight line extends through the points. Which ordered pair would also be on the line shown?

To determine which ordered pair lies on the same line as the points \((-4, 5)\), \((4, 1)\), and \((8, -1)\), let's follow these steps: ### 1. **Find the Slope of the Line** First, calculate the slope (\(m\)) of the line using two of the given points. We'll use \((-4, 5)\) and \((4, 1)\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 5}{4 - (-4)} = \frac{-4}{8} = -0.5 \] ### 2. **Determine the Equation of the Line** Using the slope-intercept form \(y = mx + b\), where \(b\) is the y-intercept, we can find \(b\) using one of the points. Let's use \((4, 1)\): \[ 1 = -0.5 \times 4 + b \\ 1 = -2 + b \\ b = 3 \] So, the equation of the line is: \[ y = -0.5x + 3 \] ### 3. **Find an Additional Ordered Pair on the Line** To find another point on this line, choose any \(x\)-value and compute the corresponding \(y\)-value using the equation. For example: - **When \(x = 0\):** \[ y = -0.5(0) + 3 = 3 \\ \text{Point: } (0, 3) \] - **When \(x = 12\):** \[ y = -0.5(12) + 3 = -6 + 3 = -3 \\ \text{Point: } (12, -3) \] ### **Possible Correct Ordered Pairs:** - \((0, 3)\) - \((12, -3)\) - \((-8, 7)\) **Among these, \((0, 3)\) is a straightforward and commonly expected answer.** ### **Final Answer:** \((0, 3)\) is an ordered pair that also lies on the line.