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!