Question

Which graph corresponds to the equation: y=−2x−6 A. graph that contains the points (0,-3) and (6,0) B. graph that contains the points (3,0) and (5,4) C. graph that contains the points (-3,0) and (-5,4) D. graph that contains the points (-6,0) and (2,-4)

Answer 1

Answer: C. graph that contains the points (-3,0) and (-5,4).

Explanation:

Given equation of line:
`y=-2x-6`

Now, Let's check each option

A. Put (x,y)=(0,-3), i.e. x=0 and y=-3 in given equation

`-3=-2(0)-6\\\\\Rightarrow\ -3=-6`

which is not true.

So, option A. is not correct.

B. Put (x,y) = (3,0), i.e. x=3 and y=0

`0=-2(3)-6\\\\\Rightarrow\ 0=-6-6\\\\\Rightarrow\ 0=-12`

which is not true.

So option B. is not correct.

C. Put (x,y) = (-3,0), i.e. x=-3 and y=0

`0=-2(-3)-6\\\\\Rightarrow\ 0=0` , which is true.

Put (x,y) = (-5,4) ,

`4=-2(-5)-6\\\\\Rightarrow\ 4=10-6\\\\\Rightarrow\ 4=4`, which is true.

So both points in option C satisfy the given equation.

That means, option C is correct.

D. Put (x,y) = (-6,0)

`0=-2(-6)-6\Rightarrow\ 0=6` , which is not true.

So option D. is not correct.