Write the equation of the line satisfiying the givrn geometric conditions.

L has y-intercept (0, 2) and is perpendicular to the line with equation 2x-3y=6

Here is my answer please check.
-2/3x-2

I can see it is wrong just by looking at the slope. The perpendicular line has a slope of 2/3, which means that L must have the negative reciprocal of that slope, or m= -3/2

To find the equation of the line that satisfies the given conditions, we need to use two key pieces of information: the y-intercept and the fact that it is perpendicular to the line with the equation 2x - 3y = 6.

1. Find the slope of the given line:
The equation of the given line is 2x - 3y = 6. To find the slope, we need to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:
2x - 3y = 6
-3y = -2x + 6
Divide both sides by -3 to isolate y:
y = (2/3)x - 2

So, the slope of the given line is 2/3.

2. Determine the slope of the perpendicular line:
Since the line we want to find is perpendicular to the given line, its slope will be the negative reciprocal of 2/3. To find the negative reciprocal, we invert the fraction and change its sign:
Negative reciprocal of 2/3 = -3/2

3. Use the slope and the y-intercept to form the equation:
We know that the line passes through the y-intercept (0, 2), and its slope is -3/2.

Using the point-slope form of a linear equation (y - y1 = m(x - x1)), we can substitute the slope (-3/2) and the coordinates (0, 2) into the equation:
y - 2 = (-3/2)(x - 0)

Simplifying this equation gives us:
y - 2 = (-3/2)x

To isolate y, we can move the -2 to the other side of the equation by adding 2 to both sides:
y = (-3/2)x + 2

Therefore, the equation of the line that satisfies the given conditions is y = (-3/2)x + 2.