Question

what is the equation of the line that is parallel to the given line and has an \\(x\\)-intercept of \\(-3\\)?

\\(y = \frac{2}{3}x + 3\\)

\\(y = \frac{2}{3}x + 2\\)

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

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

Explanation:

Find the slope of the given line

$$ m = \frac{1 - (-1)}{3 - 0} = \frac{2}{3} $$

Determine the equation of the parallel line

$$
LATEXBLOCK0
$$

Answer:

• (A) \(y = \frac{2}{3}x + 3\)
• (B) \(y = \frac{2}{3}x + 2\) (Correct answer)
• (C) \(y = -\frac{3}{2}x + 3\)
• (D) \(y = -\frac{3}{2}x + 2\)