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.

Step-by-step explanation:

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:

The line is:

Correct choice is C

2.

The line is:

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

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

Correct choice is D

3.

The line given:

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

Find its y-intercept:

The line is:

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:

The line is:

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

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.

2.

Rewrite the second line as:

The slopes are same, - 2.

3.

Rewrite the second line as:

The slopes are 4 and 1/4.

1.

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

2.

Perpendicular lines can't have same slopes.

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]

Step-by-step explanation:

b and c

step-by-step explanation:

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.