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. (simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The given line \( y = -3x + 2 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. So the slope of the line we want to find, \( m=-3 \).

Step2: Use the point - slope formula

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope. We are given the point \( (-4,-6) \), so \( x_1=-4 \) and \( y_1 = - 6 \), and \( m=-3 \).
Substitute these values into the point - slope formula:
\( y-(-6)=-3(x - (-4)) \)
Simplify the left - hand side and the right - hand side:
\( y + 6=-3(x + 4) \)

Answer:

\( y + 6=-3(x + 4) \)