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)\\)?

options:

• \\((6, 0)\\)
• \\((0, 6)\\)
• \\((-5, 0)\\)
• \\((0, -5)\\)

Explanation:

Find slope of given line

Identify two points on the red line:

$$ (-8, 6) \quad \text{and} \quad (4, -4) $$

Calculate the slope \(m\):

$$ m = \frac{-4 - 6}{4 - (-8)} = \frac{-10}{12} = -\frac{5}{6} $$

Determine parallel line equation

Parallel lines have equal slopes:

$$ m_{\text{parallel}} = -\frac{5}{6} $$

Use point-slope form with point \((-6, 10)\):

$$ y - 10 = -\frac{5}{6}(x + 6) $$

Find the x-intercept

Set \(y = 0\) for the \(x\)-axis:

$$ 0 - 10 = -\frac{5}{6}(x + 6) $$

Solve for \(x\):

$$ -10 = -\frac{5}{6}(x + 6) $$

$$ 12 = x + 6 \implies x = 6 $$

Identify the ordered pair

The point on the \(x\)-axis is:

$$ (6, 0) $$

Answer:

• (A) \((6, 0)\) (Correct answer)
• (B) \((0, 6)\)
• (C) \((-5, 0)\)
• (D) \((0, -5)\)