Question

find the equation of the line that is parallel to y = 2x - 7 and contains the point (-3,6). y = ?x +

Explanation:

Step1: Determine the slope of the parallel line

Parallel lines have the same slope. The given line \( y = 2x - 7 \) 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 2.

Step2: Use the point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope. We know that \( m = 2 \), \( x_1=-3 \), and \( y_1 = 6 \). Substitute these values into the point - slope form:
\( y-6=2(x - (-3)) \)
Simplify the right - hand side: \( y - 6=2(x + 3) \)

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y-6 = 2x+6 \)
Add 6 to both sides of the equation: \( y=2x + 6+6 \)
Simplify the right - hand side: \( y=2x+12 \)

Answer:

\( y = 2x+12 \) (So the first box is 2 and the second box is 12)