Question

find the equation of the line parallel to \\(y = \frac{2}{3}x + 4\\) that passes through the point \\((2, 1)\\) in slope-intercept form.

a.) \\(y = -\frac{3}{2}x + 4\\)

b.) \\(y = \frac{2}{3}x - \frac{4}{3}\\)

c.) \\(y = -\frac{3}{2}x + \frac{7}{2}\\)

d.) \\(y = \frac{2}{3}x - \frac{1}{3}\\)

Explanation:

Identify the slope of the parallel line

Using the Linear Equations knowledge point

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Use point-slope form to find the equation

We use the point-slope formula \(y - y_1 = m(x - x_1)\) with the point \((2, 1)\) and slope \(m = \frac{2}{3}\):

$$ y - 1 = \frac{2}{3}(x - 2) $$

Convert to slope-intercept form

We distribute the slope and solve for \(y\):

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Answer:

• a.) \(y = -\frac{3}{2}x + 4\)
• b.) \(y = \frac{2}{3}x - \frac{4}{3}\)
• c.) \(y = -\frac{3}{2}x + \frac{7}{2}\)
• d.) \(y = \frac{2}{3}x - \frac{1}{3}\) (Correct answer)