Question

for the equation \\(y + 2 = 6(x - 5)\\), the line has a slope of 6 and contains what point?

\\((5, -2)\\)
\\((-2, 5)\\)
\\((2, -5)\\)
\\((-5, 2)\\)

Explanation:

Identify the standard form

The given equation is \(y + 2 = 6(x - 5)\).
This matches the point-slope form of a linear equation.
The standard point-slope formula is:

$$y - y_1 = m(x - x_1)$$

Extract the slope

In the formula \(y - y_1 = m(x - x_1)\), \(m\) represents the slope.
Comparing \(y + 2 = 6(x - 5)\) to the standard form:

$$m = 6$$

This confirms the given slope is \(6\).

Extract the coordinates

The point \((x_1, y_1)\) lies on the line.
Compare the terms to find \(x_1\) and \(y_1\):
For the x-coordinate:

$$x - x_1 = x - 5 \implies x_1 = 5$$

For the y-coordinate:

$$y - y_1 = y + 2 \implies y - y_1 = y - (-2) \implies y_1 = -2$$

Write the final point

Combining the coordinates \((x_1, y_1)\) gives the point:

$$(5, -2)$$

This matches the first option.

Answer:

• (A) (5, -2) (Correct answer)
• (B) (-2, 5)
• (C) (2, -5)
• (D) (-5, 2)