Question

Please help me with these 5 questions!

2.
A. No
B. yes; k = -1/2 and y = -1/4x
C. yes; k = 4 and y = 4x
D. yes; k = 1/4 and y = 1/4x

6.
A. y = 5x-1
B. y = 5/2x+5
C. y = -x+5
D. y = 1/5x-1

8.

A. line a
B. line d
C. line b
D. line c

11.
What is the slope of the line through the points (–2, –1) and (8, –3)?
A. 3/2
B. 1/5
C. -3/2
D. -1/5

15.
A. line a
B. line d
B. line b
C. line c

Answer 1

Part 2) Option D. yes; k = 1/4 and y = 1/4x

Part 6) Option D. y = 1/5x-1

Part 8) Option C. line b

Part 11) Option D. -1/5

Part 15) Option A. line a

Explanation:

Part 2) we know that

A relationship between two variables, x, and y, represent a directly variation if it can be expressed in the form
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the line passes through the origin

therefore

Yes. y varies directly with x

Let

A(4,1)

The constant k is equal to

`k=y/x`

substitute

`k=1/4`

the equation is equal to

`y=(1/4)x`

Part 6) we know that

The y-intercept of the trend line is -1 (For x=0)

The slope of the trend line is positive

The x-intercept of the trend line is 5 (For y=0)

therefore

the equation is equal to

`y=(1/5)x-1`

Part 8) we have

`y+4=-(2)/(3)x`

This is the equation of a line into point slope form

The slope is negative
`m=-2/3`

Pass through the point (0,-4) ----> y-intercept

The x-intercept is equal to

`0+4=-(2)/(3)x`

`x=-4*3/2=-6`

therefore

Is the line b

Part 11)

What is the slope of the line through the points (–2, –1) and (8, –3)?

we know that

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(-3+1)/(8+2)`

`m=(-2)/(10)`

simplify

`m=-(1)/(5)`

Part 15) we have

`y=3x-2`

The slope is positive
`m=3`

The y-intercept is -2 (For x=0)

The x-intercept is (For y=0)

`0=3x-2`

`3x=2`

`x=2/3`

therefore the line is a