What is an equation of the line that passes through the point (-4,-3) and is perpendicular to the line 2x+3y=15

The equation would be y = 3/2x + 3

Step-by-step explanation:

First we have to find the slope of the original line. We can do this by solving for y.

2x + 3y = 15

3y = -2x + 15

y = -2/3x + 5

Now that we have the slope of -2/3, we know the slope of the new line will be 3/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use that and a point in point-slope form to find the equation.

y - y1 = m(x - x1)

y + 3 = 3/2(x + 4)

y + 3 = 3/2x + 6

y = 3/2x + 3

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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