Question

which linear function represents the line given by the point-slope equation \\(y - 2 = 4(x - 3)\\)?

\\(f(x) = 6x - 1\\)
\\(f(x) = 8x - 6\\)
\\(f(x) = 4x - 14\\)
\\(f(x) = 4x - 10\\)

Explanation:

Distribute the slope on the right side

Using the Point-Slope Form knowledge point

$$ y - 2 = 4(x - 3) \implies y - 2 = 4x - 12 $$

Isolate y to find the function form

Using the Slope-Intercept Form knowledge point

$$ y = 4x - 12 + 2 \implies y = 4x - 10 $$

Write in function notation

Using the Slope-Intercept Form knowledge point

$$ f(x) = 4x - 10 $$

Answer:

• (A) \(f(x) = 6x - 1\)
• (B) \(f(x) = 8x - 6\)
• (C) \(f(x) = 4x - 14\)
• (D) \(f(x) = 4x - 10\) (Correct answer)