Question

1. write an equation of the line that passes through (6, -4) and is parallel to the line ( y = \frac{1}{3}x + 3 ). an equation of the parallel line is ( y = square ).

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have the same slope. The given line is \( y = \frac{1}{3}x + 3 \), so its slope \( m=\frac{1}{3} \). The parallel line will also have \( m = \frac{1}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(6,-4) \) and \( m=\frac{1}{3} \).
Substitute the values: \( y-(-4)=\frac{1}{3}(x - 6) \)

Step3: Simplify the equation

Simplify \( y + 4=\frac{1}{3}x-2 \)
Subtract 4 from both sides: \( y=\frac{1}{3}x-2 - 4 \)
\( y=\frac{1}{3}x-6 \)

Answer:

\( y=\frac{1}{3}x - 6 \)