Answer:
Part 40) [tex]y=-2x+9[/tex]
Part 41) [tex]y=5x+6[/tex]
Part 42) [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]
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
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
The slope of the given line is
[tex]m=-2[/tex]
step 2
Find the y-intercept b
we have
[tex]m=-2[/tex]
[tex](4,1)[/tex]
substitute in the linear equation
[tex]1=(-2)4+b[/tex]
solve for b
[tex]b=1+8[/tex]
[tex]b=9[/tex]
step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have
[tex]m=-2[/tex]
[tex]b=9[/tex]
substitute
The equation of the line is
[tex]y=-2x+9[/tex]
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
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
The slope of the given line is
[tex]m=5[/tex]
step 2
Find the y-intercept b
[tex]b=6[/tex] ----> 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
[tex]m=5[/tex]
[tex]b=6[/tex]
substitute in the linear equation
[tex]y=5x+6[/tex]
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
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
The slope of the given line is
[tex]m=\frac{2}{3}[/tex]
step 2
Find the y-intercept b
we have
[tex]m=\frac{2}{3}[/tex]
[tex](-5,-2)[/tex]
substitute in the linear equation
[tex]-2=(\frac{2}{3})(-5)+b[/tex]
solve for b
[tex]-2=-\frac{10}{3}+b[/tex]
[tex]b=-2+\frac{10}{3}[/tex]
[tex]b=\frac{4}{3}[/tex]
step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have
[tex]m=\frac{2}{3}[/tex]
[tex]b=\frac{4}{3}[/tex]
substitute
The equation of the line is
[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]
