Question

write the equation of a line parallel to $y = -3x + 9$ and passing through the point $(2, 6)$. select the correct answer $y = -3x + 12$ $y = -\frac{1}{3}x + 12$ $y = 3x + 12$ $y = \frac{1}{3}x + 12$

Explanation:

Step1: Recall parallel line slope

Parallel lines have equal slopes. The given line \( y = -3x + 9 \) has a slope \( m = -3 \), so the parallel line also has \( m = -3 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(2,6) \) and \( m=-3 \).
Substitute values: \( y - 6=-3(x - 2) \)

Step3: Simplify the equation

Expand the right - hand side: \( y - 6=-3x + 6 \)
Add 6 to both sides: \( y=-3x + 6 + 6\), so \( y=-3x + 12 \)

Answer:

\( y = - 3x+12 \) (the first option: \( y=-3x + 12 \))