Question

find an equation for the line with the given properties. express your answer using either the general form or the slope - intercept form of the equation of a line. parallel to the line y = 5x, containing the point (-6, 6) the equation is \boxed{}. (type an equation. simplify your answer.)

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The line \( y = 5x \) is in slope - intercept form \( y=mx + b \) where \( m = 5 \). So the slope of the line we want to find is also \( m = 5 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-6,6) \) and \( m = 5 \). Substitute these values into the formula:
\( y - 6=5(x - (-6)) \)
Simplify the right - hand side: \( y - 6=5(x + 6) \)

Step3: Convert to slope - intercept form (or general form)

Expand the right - hand side: \( y-6 = 5x+30 \)
Add 6 to both sides: \( y=5x + 36 \)

Answer:

\( y = 5x+36 \)