could you please check this answer for me and correct. thanks

given equation point slope form linear equation to use to do question. y-3 = 3(x+1)
question rewrite this equation in standard form
y- 3 + 3 = 3x - 3x +3 + 3
-3x+ y = 6 collect all variables on one side and constants on other for standard form.

next question said, what is the x intercept of this line? would it be talking about -1 from original equation or -3x + y = 6
-3x = y(0) = 6
x = -2 x inter is -2
thanks for your help. ann

-3x + y = 6 is correct, but we usually start with a positive x term, so

3x - y = -6

for the x-intercept, let y = 0 , (you are on the x-axis)
3x - 0 = -6
x = -2

the x-intercept is -2

yes, you were right.

Reiny, thank you very much for your help. ann

Let's go through your answers and correct them.

To rewrite the equation in standard form, we need to eliminate any parentheses and simplify the equation. Starting with the given equation:

y - 3 = 3(x + 1)

Distribute the 3 on the right side:

y - 3 = 3x + 3

Next, bring all the terms to one side of the equation. Subtract y from both sides:

-y + y - 3 = 3x + y - 3

Simplify:

-3 = 3x + y - 3

Rearrange the terms so that the x and y variables appear before the constant term:

3x + y = -3 + 3

Combine like terms:

3x + y = 0

So, the correct equation in standard form is 3x + y = 0.

Now, let's move on to the question about the x-intercept of the line. The x-intercept is the point where the line crosses the x-axis. To find it, we need to set y = 0 and solve for x in the standard form equation:

3x + y = 0

Substituting y with 0:

3x + 0 = 0

Simplify:

3x = 0

Divide both sides by 3:

x = 0

Therefore, the x-intercept of the line is x = 0, not x = -2.

I hope this helps clarify your doubts. If you have any more questions, feel free to ask!