Question

line c has an equation of $y = \frac{4}{3}x + 9$. line d is parallel to line c and passes through $(-4, -4)$. what is the equation of line d? write the equation in slope-intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Determine slope of line d

Parallel lines have equal slopes. Line c has slope \( \frac{4}{3} \), so line d also has slope \( m = \frac{4}{3} \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-4,-4) \) and \( m=\frac{4}{3} \).
Substitute values: \( y - (-4)=\frac{4}{3}(x - (-4)) \), which simplifies to \( y + 4=\frac{4}{3}(x + 4) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y+4=\frac{4}{3}x+\frac{16}{3} \).
Subtract 4 (which is \( \frac{12}{3} \)) from both sides: \( y=\frac{4}{3}x+\frac{16}{3}-\frac{12}{3} \).
Simplify the right - hand side: \( y=\frac{4}{3}x+\frac{4}{3} \).

Answer:

\( y=\frac{4}{3}x+\frac{4}{3} \)