Answer:
Part 40) 
Part 41) 
Part 42) 
Step-by-step explanation:
Remember that 
If two lines are parallel, then their slopes are the same
Part 40) Write an equation of the line that passes through the given point 
and is parallel to the given line
we have
Point (4,1)
Given line y=-2x+7
step 1
Find the slope of the given line
The given line is a equation of the line in slope intercept form

where
m is the slope 
b is the y-intercept
so
The slope of the given line is

step 2
Find the y-intercept b
we have
 
 

substitute in the linear equation

solve for b


step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have
 
 

substitute 
The equation of the line is

Part 41) Write an equation of the line that passes through the given point 
and is parallel to the given line
we have
Point (0,6)
Given line y=5x-3
step 1
Find the slope of the given line
The given line is a equation of the line in slope intercept form

where
m is the slope 
b is the y-intercept
so
The slope of the given line is

step 2
Find the y-intercept b
 ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)
 ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)
step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have
 
 
 
 
substitute in the linear equation

Part 42) Write an equation of the line that passes through the given point 
and is parallel to the given line
we have
Point (-5,-2)
Given line y=(2/3)x+1
step 1
Find the slope of the given line
The given line is a equation of the line in slope intercept form

where
m is the slope 
b is the y-intercept
so
The slope of the given line is

step 2
Find the y-intercept b
we have


substitute in the linear equation

solve for b



step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have


substitute 
The equation of the line is
