Question

knewton alta
2.2c linear equations in one...
current objective
write the equation of a line parallel to a given line
question
find the equation of the line through (3, -6) which is parallel to the line ( y = -7x + 5 ).
give your answer in the form ( y = mx + b ).

Explanation:

Step1: Determine the slope of the parallel line

Parallel lines have the same slope. The given line is \( y = -7x + 5 \), which is in the 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 the point - slope form to find the equation

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(3,-6) \) and \( m=-7 \).
Substitute the values into the point - slope form:
\( y - (-6)=-7(x - 3) \)
Simplify the left - hand side: \( y + 6=-7(x - 3) \)

Step3: Simplify to slope - intercept form (\( y=mx + b \))

Expand the right - hand side: \( y+6=-7x + 21 \)
Subtract 6 from both sides: \( y=-7x+21 - 6 \)
Simplify the right - hand side: \( y=-7x + 15 \)

Answer:

\( y=-7x + 15 \)