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What is an equation of the line that passes through the points (0,3) and (5,−3)? Put your answer in fully reduced form.

User Plok
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Using the "gradient, two-point form", we have:

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
From the given data, we have that

y2 = - 3 \\ y1 = 3 \\ x2 = 5 \\ x1 = 0
Therefore, substitute in the given values:
We have that:

(y - (3))/(x - (0)) = (( - 3) - (3))/((5) - (0))
Simplify further

(y - 3)/(x) = ( - 6)/(5)
Multiply both sides by the LCM, 5x:

5x( (y - 3)/( x) ) = 5x( ( - 6)/(5) )
Simplify:

5( y - 3) = x( - 6)

5y - 15 = - 6x
Note that the equation of a straight line is given by Ax + By = C where A and B are coefficients of x and y respectively. C is the constant. Hence:
6x+5y=15
User Toasty
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