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larisa86 [58]
3 years ago
5

Which equation has a graph that is perpendicular to the graph of -x + 6y = -12?

Mathematics
2 answers:
Readme [11.4K]3 years ago
6 0
<h2>C</h2>

Step-by-step explanation:

Let l_{1} be the equation of the line with slope m_{1} and let l_{2} be the equation of the line with slope m_{2}.

As we know,for two lines l_{1} and l_{2} to be perpendicular,

m_{1}\times m_{2} =-1

In the given problem,slope of given line=m_{1}=\frac{-6}{-1}=6

For option a,slope =m_{2}=\frac{-6}{1} =-6

In this case,m_{1}\times m_{2}=6\times -6=-36

So,option a is incorrect.

For option b,slope =m_{2}=\frac{6}{1} =6

In this case,m_{1}\times m_{2}=6\times 6=36

So,option b is incorrect.

For option c,slope =m_{2}=\frac{-1}{6} =\frac{-1}{6}

In this case,m_{1}\times m_{2}=6\times \frac{-1}{6}=-1

So,option c is correct.

For option d,slope =m_{2}=\frac{1}{6} =\frac{1}{6}

In this case,m_{1}\times m_{2}=6\times \frac{1}{6}=1

So,option d is incorrect.

serious [3.7K]3 years ago
3 0

Answer:

c) 6x + y = -52  is required equation perpendicular to the given equation.

Step-by-step explanation:

If the equation is of the form    : y = mx  + C.

Here m = slope of the equation.

Two equations are said to be perpendicular if the product of their respective slopes is -1.

Here, equation 1 :  -x + 6y = -12

or, 6y = -12  + x

or, y = (x/6)  - 2

⇒Slope of line 1 = (1/6)

Now, for equation 2  to be  perpendicular:

Check for each equation:

a. x + 6y = -67       ⇒  6y = -67  - x

or, y = (-x/6)  - (67/6)      ⇒Slope of line 2 = (-1/6)

but \frac{1}{6} \times \frac{-1}{6}  \neq -1

b. x - 6y = -52   ⇒  -6y = -52  - x

or, y = (x/6)  + (52/6)      ⇒Slope of line 2 = (1/6)

but \frac{1}{6} \times \frac{1}{6}  \neq -1

c. 6x + y = -52    

or, y =y = -52  - 6x      ⇒Slope of line 2 = (-6)

\frac{1}{6} \times (-6)  =  -1

Hence, 6x + y = -52  is required equation 2.

d. 6x - y = 52  ⇒  -y = 52  - 6x

or, y = 6x   - 52      ⇒Slope of line 2 = (6)

but \frac{1}{6} \times 6  \neq -1

Hence,  6x + y = -52  is  the  only required equation .

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