Question

the equation for line k can be written as y + 3 = -3(x - 7). line ℓ includes the point (4, -4) and is parallel to line k. what is the equation of line ℓ?
write the equation in slope-intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line k

The equation of line k is \( y + 3 = -3(x - 7) \). In point - slope form \( y - y_1=m(x - x_1) \), the slope \( m \) of line k is - 3. Since parallel lines have the same slope, the slope of line \( l \) ( \( m_l \)) is also - 3.

Step2: Use point - slope form for line l

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

Step3: Convert to slope - intercept form (\( y=mx + b \))

Expand the right - hand side: \( y + 4=-3x+12 \)
Subtract 4 from both sides: \( y=-3x + 12-4 \)
Simplify the right - hand side: \( y=-3x + 8 \)

Answer:

\( y=-3x + 8 \)