Question

write the equation of the line that goes through the point \\((2, -4)\\) and is parallel to \\(y = 3x + 2\\)

\\(y = 3x - 10\\)
\\(y = -3x + 2\\)
\\(y = -4x + 2\\)
\\(y = x\\)

Explanation:

Identify the slope of the parallel line

Using the Slope-Intercept Form and Linear Equations knowledge points:
The given line is \(y = 3x + 2\).
Its slope is \(m = 3\).
Parallel lines have equal slopes.
Thus, our line has slope \(m = 3\).

Write the equation using point-slope form

Using the Point-Slope Form knowledge point:
We use the point \((2, -4)\) and slope \(m = 3\).

$$ y - y_1 = m(x - x_1) $$

$$ y - (-4) = 3(x - 2) $$

$$ y + 4 = 3(x - 2) $$

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point:
We simplify the equation to solve for \(y\).

$$ y + 4 = 3x - 6 $$

$$ y = 3x - 10 $$

Answer:

• (A) \(y = 3x - 10\) (Correct answer)
• (B) \(y = -3x + 2\)
• (C) \(y = -4x + 2\)
• (D) \(y = x\)