Question

the point-slope form of a line that has a slope of \\(\frac{2}{3}\\) and passes through point \\((6, 0)\\) is shown below.

\\y - 0 = \frac{2}{3}(x - 6)\\

what is the equation in slope-intercept form?

\\(y = \frac{2}{3}x - 12\\)
\\(y = \frac{2}{3}x - 6\\)
\\(y = \frac{2}{3}x - 4\\)
\\(y = \frac{2}{3}x - 8\\)

Explanation:

Distribute the slope on the right side

$$ y - 0 = \frac{2}{3}(x - 6) $$

$$ y - 0 = \frac{2}{3}x - \frac{2}{3}(6) $$

Simplify the constant term

$$ \frac{2}{3}(6) = 4 $$

$$ y = \frac{2}{3}x - 4 $$

Answer:

• (A) \(y = \frac{2}{3}x - 12\)
• (B) \(y = \frac{2}{3}x - 6\)
• (C) \(y = \frac{2}{3}x - 4\) (Correct answer)
• (D) \(y = \frac{2}{3}x - 8\)