Question

Which equation represents a line that passes through (–9, –3) and has a slope of –6?

y – 9 = –6(x – 3)

y + 9 = –6(x + 3)

y – 3 = –6(x – 9)

y + 3 = –6(x + 9)

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Answer 1

Answer: D. y + 3 = –6(x + 9)

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Explanation:

Answer 2

Hello!

The answer is:

The last equation,

`y+3=-6(x+9)`

Why?

To find which of the given equations represents a line that passes through the point (-9,-3) and has a slope of -6, we need to find an equation that can be satisfied by evaluating the given point.

We can see that the only equation that can be satisfied evaluating the point (-9,-3) is the last equation:

`y+3=-6(x+9)`

Evaluating the point, we have:

`-3+3=-6*(-9+9)`

`0=-6*(0)`

`0=0`

We can see that the equation is satisfied!

Also, we can see that evaluating the point into the other equations, they will not be satisfied.

Let's prove that:

Evaluating:

First equation:

`y-9=-6(x-3)\\-3-9=-6*(-9-3)\\-12=-6*(-12)=72`

The equation is not satisfied.

Second equation:

`y+9=-6(x+3)\\-3+9=-6*(-9+3)\\6=-6*(-6)=36`

The equation is not satisfied.

Third equation:

`y-3=-6(x-9)`

`-3-3=-6(-9-9)`

`-6=-6(-18)=108`

The equation is not satisfied.

Hence, the correct option is the last option, the equation that represents a line that passes through (–9, –3) and has a slope of –6 is the last equation:

`y+3=-6(x+9)`

Have a nice day!

Note: I have attached a picture for better understanding.