Your idea is correct.

You tried to find the slope of the line.

Then you used that slope in the point-slope form of the equation of the line.

But your solution/answer is wrong.

Mistakes in the Algebra. I'd say, mistakes due to skipping steps.

-4 - (-2)

--------- = -2/3

3 - 6

Maybe if you did not skip one step you could have got the correct slope.

Like this:

-4 - (-2)

--------- = -2/(-3) = 2/3 <---the correct slope is positive.

3 - 6

next

y - (-2) = (2/3)(x - 6)

y - (-2) = (2/3)x -(2/3)6

y - (-2) = (2/3)x -4

y -(-2) +(-2) = (2/3)x -4 +(-2)

y = (2/3)x -6 <----answer.

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Of course it is okay to skip steps. But if you are not that good yet, maybe it's good for you to do it step by step.

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Also, to check if your answer is correct, you test your answer with the given data.

So your answer is

y = -(2/3)x +7

See if that is correct by plugging, say, (6,-2) into your answer.

Like so,

-2 = -(2/3)6 +7

-2 = -4 +7

-2 = 3

No, they are not equal, so your answer is not correct.