MATH SOLVE

4 months ago

Q:
# 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- 1Question 6 options:y = -3x + 14y = x3+ 14y = 3x + 23y = -3x + 23Question 7 (1 point) Question 7 UnsavedWhat is the equation of a line that passes through the point (4,2) and is parallel to the line whose equation is y = x3- 1Question 7 options:y = -3x + 14y = x3+ 14y = 3x - 23y = -3x - 23

Accepted Solution

A:

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

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