Glencoe Algebra 2, Chapter 2, 2.4, Section 2.4, Problem 38

Given
a line L1 (let us assume) passes through (-3, -1) and is parallel to the line L2 (let us assume) that passes through (3, 3) and (0, 6).
we need to find the equation of L1?

sol:
First we need to find the slope of the line L2 that passes through (3, 3) and (0, 6).
m_2 = (6-3) / (0-3) = 3/ -3 = -1
as the line L1 and L2 are parallel so their slopes are equal
so the slope of the line L1 is m = -1 and it passes
through the point (-3, -1).
the line equation is given as the slope-intercept from
y= mx +b
=>y = (-1)x+b------------(1)
as the line (1) passes through the point (-3, -1) we get the value of b on substituting as follows
-1 = (-1)(-3) +b
=> b = -1-3 = -4
so the equation of the line from (1) is
y = -x -4 is the sloution