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

Using the Slope of a Line knowledge point

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

Determine the slope of the parallel line

Using the Parallel Line Equations knowledge point

$$ m_{\text{parallel}} = m = \frac{2}{3} $$

Identify the point on the parallel line

The parallel line has an \(x\)-intercept of \(-3\), which corresponds to the coordinate point:

$$ (x_1, y_1) = (-3, 0) $$

Write the equation of the parallel line

Using the Point-Slope Form knowledge point

$$
LATEXBLOCK0
$$

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