Question

consider the line \\(y = -6x + 2\\).

find the equation of the line that is parallel to this line and passes through the point \\((-5, 3)\\).

find the equation of the line that is perpendicular to this line and passes through the point \\((-5, 3)\\).

equation of parallel line:
equation of perpendicular line:

Explanation:

Identify the slope of the given line

Using the Linear Functions knowledge point
The given line is:

$$y = -6x + 2$$

This is in slope-intercept form \(y = mx + b\), where the slope is:

$$m = -6$$

Find the equation of the parallel line

Using the Parallel Lines knowledge point

$$
LATEXBLOCK0
$$

Find the equation of the perpendicular line

Using the Perpendicular Lines knowledge point

$$
LATEXBLOCK1
$$

Answer:

Question 1

Equation of parallel line: <blank>\(y = -6x - 27\)</blank>

Question 2

Equation of perpendicular line: <blank>\(y = \frac{1}{6}x + \frac{23}{6}\)</blank>