Question

PLEASE HELP. IM MAJORLY STRUGGLING. 100 POINTS.

Pt. 1 - Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
1. (2,-1) ; y = -3/2x + 6
a. y = -3/2x + 1
b. y = -3/2x - 1
c. y = -3/2x + 2
d. y = -3/2x + 4

2. (4,2) ; x = -3
a. y = 2
b. y = 2x + 4
c. y = 4x
d. x = 4

3. (-2,3) ; y = 1/2x - 1
a. y = 1/2x + 1
b. y = -2x - 1
c. y = 1/2x - 1
d. y = -1/2x - 1

4. (5,0) ; y + 1 = 2(x-3)
a. y = -1/2x + 5
b. y = 2x - 5
c. y = 1/2x - 2
d. y = -1/2x + 5/2


Pt. 2 - Determine whether the graphs of the given points are parallel, perpendicular, or neither.
1. y = x + 11 and y = -x + 2

2. y = -2x + 3 and 2x + y = 7

3. y = 4x - 2 and -x + 4y = 0

Pt. 3 - Determine whether the statement is always, sometimes, or never true.
1. Two lines with positives slopes are always parallel.

2. Two lines with the same slope and different y-intercepts are perpendicular.

Answer 1

• See below

Explanation:

Part 1

1. Given line:

y = -3/2x + 6

Parallel line has same slope of -3/2 and passes through the point (2, -1).

Find its y-intercept:

• - 1 = -3/2*2 + b
• -1 = - 3 + b
• b = 2

The line is:

• y = -3/2x + 2

Correct choice is C

2.

The line is:

• x = -3

It has undefined slope and is parallel to the y-axis.

The line parallel to this and passing through the point (4, 2) is:

• x = 4

Correct choice is D

3.

The line given:

• y = 1/2x - 1

Parallel line has same slope of 1/2 and passes through the point (-2, 3).

Find its y-intercept:

• 3 = 1/2(-2) + b
• 3 = - 1 + b
• b = 4

The line is:

• y = -1/2x + 4

Non of the answer choices match this, something is wrong with given

4.

Given line:

y + 1 = 2(x - 3),

Converting this to slope-intercept:

y = 2x - 6 - 1

y = 2x - 7

The line parallel to this has the slope of 2 and passes through the point (5, 0)

Its y-intercept is:

• 0 = 2*5 + b
• b = - 10

The line is:

• y = 2x - 10

Non of the answer choices match this, something is wrong with given

Part 2

Compare the slopes of the lines. They are parallel if slopes are same, perpendicular if the product of the slopes is -1.

1.

The slopes are 1 and - 1, so their product is - 1.

• The lines are perpendicular

2.

Rewrite the second line as:

• 2x + y = 7 ⇒ y = -2x + 7

The slopes are same, - 2.

• The lines are parallel.

3.

Rewrite the second line as:

• - x + 4y = 0 ⇒ 4y = x ⇒ y = 1/4x

The slopes are 4 and 1/4.

• The lines are neither parallel nor perpendicular.

Part 3

1.

Parallel lines have same slopes, they can be negative too.

• It can sometimes be true, when positive slopes are same.

2.

Perpendicular lines can't have same slopes.

• It is never true.

Answer 2

PT:1

1. (2,-1) ;

y = -3/2x + 6.....[1]

now

comparing above equation with y=mx+c we get,

m=-3/2

since another line is parallel ;

slope of another line is m=M=-3/2

since it passes through (2,-1)

now

equation of line is;

y-y1=m(x-x1)

y-(-1)=-3/2 (x-2)

y+1=-3/2x+3

y=-3/2 x+3-1

c. y=-3/2 x +2 is a required equation.

2. (4,2) ;

x = -3

it means parallel to y-axis

m=y/x

slope of another line is same so,slope is 0/-3=0

since it passes through (4,2)

now

equation of line is;

y-y1=m(x-x1)

y-2=0 (x-4)

a. y=2 is a required equation.

3. (-2,3) ;

y = 1/2x - 1

comparing above equation with y=mx+c we get,

m=1/2

since another line is parallel ;

slope of another line is m=M=1/2

since it passes through (-2,3)

now

equation of line is;

y-y1=m(x-x1)

y-3=1/2 (x-(-2))

y-3=1/2 x+1

y=1/2 x +1+3

a. y=1/2x +4 is a required equation.[not sure]

4. (5,0) ;

y + 1 = 2(x-3)

y+1=2x-6

y=2x-6+1

y=2x-5

comparing above equation with y=mx+c we get,

m=2

since another line is parallel ;

slope of another line is m=M=2

since it passes through (5,0)

now

equation of line is;

y-y1=m(x-x1)

y-0=2 (x-5)

b. y=2(x-5) is a required equation.[not sure]

Explanation: