Question

use the given conditions to write an equation for the line in point - slope form and in slope - intercept form. passing through (-4, -6) and parallel to the line whose equation is y = -3x + 2... write an equation for the line in point - slope form. y + 6 = -3(x + 4) (simplify your answer. use integers or fractions for any numbers in the equation.) write an equation for the line in slope - intercept form. (simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. We know the slope \( m \) from the parallel line (parallel lines have the same slope). The given line \( y=-3x + 2 \) has a slope \( m=-3 \). We also have the point-slope form \( y + 6=-3(x + 4) \).

Step2: Expand the point-slope form

Expand \( y + 6=-3(x + 4) \):
\( y+6=-3x-12 \)

Step3: Solve for y

Subtract 6 from both sides:
\( y=-3x-12 - 6 \)
\( y=-3x-18 \)

Answer:

\( y = -3x - 18 \)