Find the point slope form of the equation of the line that passes through the point (0,2) and it has the slope m = -3 ?

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You need to use the point slope form of equation of the line, such that:

`y = m(x - x_0) + y_0`

The problem provides the slope `m = -3` and coordinates of point, `x_0 = 0, y_0 = 2` , such that:

`y = -3(x - 0) + 2 => y = -3x + 2`

**Hence, evaluating the point slope form of equation of the line, under the given conditions, yields `y = -3x + 2.` **

There are two basic forms of an equation for a line: the point-slope and the standard form (the standard is sometimes also called the slope-intercept form).

The Point-Slope form of an equation:

(y-y1) = m(x-x1) (2)

where m is the slope and (x1,y1) is the given point.

We'll substitute the slope and given point in (2):

y - 2 = -3(x - 0)

We'll remove the brackets:

y - 2 = -3x + 0

We'll put the equation in the standard form by adding 2 both sides:

y = -3x + 2

Standard form of the equation is: y = -3x + 2

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