Write in slope-intercept form an equation of a line passing through the point A( 0,2) and perpendicular to y=2x ?

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you want a line with slope -1/2, passing through (0,2)

So the point-slope form of the line is
y-2 = -1/2 (x-0)

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).

Given that the line is perpendicular to y = 2x, we know that the slope of the line we're looking for is the negative reciprocal of 2 (the slope of the given line).

The negative reciprocal of 2 is -1/2. So, the slope (m) of our desired line is -1/2.

Now that we have the slope, we can use the point-slope form of a line to write the equation. The point-slope form is:
y - y1 = m(x - x1)

We are given a point A(0,2), so plugging it into the point-slope form, we get:
y - 2 = (-1/2)(x - 0)

Simplifying further:
y - 2 = (-1/2)x

To convert this equation into slope-intercept form, we isolate y on one side:
y = (-1/2)x + 2

Therefore, the equation of the line passing through point A(0,2) and perpendicular to y = 2x in slope-intercept form is y = (-1/2)x + 2.