Question

consider the line \\(y = \frac{4}{7}x + 6\\).

find the equation of the line that is perpendicular to this line and passes through the point \\((-4, -5)\\).

find the equation of the line that is parallel to this line and passes through the point \\((-4, -5)\\).

equation of perpendicular line:
equation of parallel line:

Explanation:

Identify the slope of the given line

$$ y = -\frac{4}{7}x + 6 \implies m_1 = -\frac{4}{7} $$

Find the equation of the perpendicular line

$$
LATEXBLOCK0
$$

Find the equation of the parallel line

$$
LATEXBLOCK1
$$

Answer:

Question 1

Equation of perpendicular line: <blank>\(y = \frac{7}{4}x + 2\)</blank>

Question 2

Equation of parallel line: <blank>\(y = -\frac{4}{7}x - \frac{51}{7}\)</blank>