using y - 3 = 3(x +1) what point does this line pass through, which is the basis of this equation? Show all steps.  Thanks

Expert Answers

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The problem provides the equation of a line. You need to remember that there exists several forms in which a equation of a line can be given. The provided form of equation follows the pattern of the point slope form. You need to compare the provided form of the equation to the point slope form, such that:

`y - y_0 = m(x - x_0)` (point slope form)

`y - 3 = 3(x + 1)` (provided form)

Comparing these forms yields that the given line passes through the point whose coordinates are `x_0 = -1` and `y_0 = 3` .

Hence, observing the given equation to evaluate the point the provided line passes through yields that this point is `(-1,3)` .

You should notice that if you draw a line, parallel to x axis, at `y = 3` , it intersects the red line at point, whose x coordinate is `x = -1` (drop a perpendicular line to x axis, from the intersection point between the line `y=3 ` and `y - 3 = 3(x + 1))` .

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