Find an equation of the line that passes through the pint (-3,-2) and is parallel to 2x=3-5y

The Answer is: y = -2/5x - 16/5

Step-by-step explanation:

Given point: (-3, -2)

Given line:

2x = 3 - 5y

Solve for y, to get the slope m. The parallel line will have the same slope.

2x = 3 - 5y

-5y + 3 = 2x

-5y = 2x - 3

y = -2/5x - 3/5, the slope is -2/5.

Use the point slope form using  -2/5 and point (-3, -2) to find the new equation:

y - y1 = m(x - x1)

y - (-2) = -2/5(x - (-3))

y + 2 = -2/5x - 6/5

y = -2/5x - 6/5 - 2

y = -2/5x - 6/5 - 10/5

y = -2/5x - 16/5

Proof:

Solve for f(-3):

f(x) = -2/5x - 16/5

f(-3) = -2/5(-3) - 16/5

f(-3) = 6/5 - 16/5

f(-3) = -10/5 = -2, giving the point (-3, -2)

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