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 ?
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