Question

Which of the following are equations for the line shown below? Check all that

apply
(-1,5)
O
A. y-2 = -0.75(x-3)
B. y-5 = -0.75(x-1)
C. y-3 = -0.75(x - 2)
D. y-5-0.75(x+1)

Answer 1

Hello!

The answer is:

The correct options are:

A)
`y-2=-0.75(x-3)`

and

D)
`y-5=-0.75(x+1)`

Why?

To find the correct answers, we need to find a equation that meet the following charactheristics:

From the graph we can se that the function:

- Has a negative slope (is decreasing)

- Pass throught the points: (-1,5) and (3,2)

Now, discarding from the given options, we have:

A.

`y-2=-0.75(x-3)`

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

`5-2=-0.75(-1-3)`

`3=-0.75(-4)`

`3=3`

Evaluating (3,2):

`2-2=-0.75(3-3)`

`0=-0.75(0)`

`0=0`

We have that the equation is satisfied, so, the line pass through the given points.

Hence, we have that the equation A is an equation of the line shown.

B.

`y-5=-0.75(x-1)`

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

`5-5=-0.75(-1-1)`

`0=-3.5`

Hence, we have that since the equation is not satisfied, the line shown is not passing through the point (-1,5) meaning that the equation is not an equation of the line shown.

So, we have that the equation B is not equation of the line shown.

C.

`y-3=-0.75(x-2)`

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

`5-3=-0.75(-1-2)`

`2=-0.75(-3)`

`2=2.25`

Hence, we have that since the equation is not satisfied, the line shown is not passing through the point (-1,5) meaning that the equation is not an equation of the line shown.

So, we have that the equation B is not equation of the line shown.

D.

(assuming you committed a mistake writing the options and the equality sign is missing)

`y-5=-0.75(x+1)`

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

`5-5=-0.75(-1+1)`

`0=-0.75(0)`

`0=0`

Evaluating (3,2)

`2-5=-0.75(3+1)`

`-3=-0.75(4)`

`-3=-3`

We have that the equation is satisfied, so, the line pass through the given points.

Hence, we have that the equation B is an equation of the line shown.

Finally, we have that the correct options are:

A)
`y-2=-0.75(x-3)`

and

D)
`y-5=-0.75(x+1)`

Have a nice day!