Question

find the equation of the line that is parallel to y = 7x - 6 and contains the point (3,22). y = ?x +

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The given line \( y = 7x - 6 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. So the slope \( m \) of the line we want to find is also 7.

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(3,22) \) and \( m = 7 \).
Substitute the values into the point - slope form:
\( y-22 = 7(x - 3) \)

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y-22=7x-21 \)
Add 22 to both sides of the equation: \( y=7x - 21 + 22 \)
Simplify the right - hand side: \( y=7x+1 \)

Answer:

\( y = 7x+1 \)