What is the equation of a line that passes through the point (4,2) and is perpendicular to the line whose equation is y = x3 - 1 question 6 options: y = -3x + 14 y = x3 + 14 y = 3x + 23 y = -3x + 23 question 7 (1 point) question 7 unsaved what is the equation of a line that passes through the point (4,2) and is parallel to the line whose equation is y = x3 - 1 question 7 options: y = -3x + 14 y = x3 + 14 y = 3x - 23 y = -3x - 23

Part A)
the correct question  is
What is the equation of a line that passes through the point (4,2) and is perpendicular to the line whose equation is y = (x/3)- 1

we have that
y = (x/3)- 1  

step 1
find the slope m
m=(1/3)
we know that
if two lines are perpendicular
so 
the slopes 
m1*m2=-1
then 
(1/3)*m2=-1
m2=-3

step 2
with m=-3 and the point (4,2) find the equation of the line
y-y1=m*(x-x1)------> y-2=-3*(x-4)----> y-2=-3x+12----> y=-3x+14

the answer part A) is
y=-3x+14

Part B)
the correct question  is
What is the equation of a line that passes through the point (4,2) and is parallel to the line whose equation is y = (x/3)- 1

we have that
y = (x/3)- 1  

step 1
find the slope m
m=(1/3)
we know that
if two lines are parallel
so 
the slopes 
m1=m2
then 
m2=(1/3)

step 2
with m=(1/3) and the point (4,2) find the equation of the line
y-y1=m*(x-x1)------> y-2=(1/3)*(x-4)----> y-2=(1/3)x-(4/3)
y=(1/3)x-(4/3)+2-----> y=(1/3)x+(2/3)

the answer part B) is
y=(1/3)x+(2/3)

using a graph tool
see the attached figure

Distance=slopeslope is -2/4which equals-1/2the distance between these two points is -1/2