SOLUTION: Write the equation of the line L satisfying the given geometric conditions. L has Y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6 I am not sure exac

Question 146253: Write the equation of the line L satisfying the given geometric conditions.
L has Y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6
I am not sure exactly what they are asking for can you please help me with this.
thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Solve for y.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point

.

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 2 to both sides.

Combine like terms.

So the equation of the line perpendicular to that goes through the point

is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the perpendicular line (green) through the point

.

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