Question

which is the ordered pair for the point on the x-axis that is on the line parallel to the given line and through the given point (-6, 10)? \bigcirc\\ (6, 0) \bigcirc\\ (0, 6) \bigcirc\\ (-5, 0) \bigcirc\\ (0, -5)

Explanation:

Step1: Find slope of given line

Points on given line: \((-8, 6)\) and \((4, -4)\). Slope \(m = \frac{-4 - 6}{4 - (-8)} = \frac{-10}{12} = -\frac{5}{6}\). Parallel lines have same slope.

Step2: Equation of new line

Using point-slope form \(y - y_1 = m(x - x_1)\) with \((-6, 10)\) and \(m = -\frac{5}{6}\):
\(y - 10 = -\frac{5}{6}(x + 6)\). Simplify: \(y = -\frac{5}{6}x - 5 + 10\) → \(y = -\frac{5}{6}x + 5\).

Step3: Find x-intercept (y=0)

Set \(y = 0\): \(0 = -\frac{5}{6}x + 5\). Solve for \(x\): \(\frac{5}{6}x = 5\) → \(x = 6\). So ordered pair is \((6, 0)\).

Answer:

\((6, 0)\)