Question

Writing the Standard Form of a Line

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Write the equation of the line that passes through the points (8, -1) and (2,-5) in standard form, given that the point
slope form is y + 1 = 2/3 (x – 8).
____x + ____y = ____

Answer 1

`2x-3y = 19`

Explanation:

In standard form, represented by the formula
`Ax+By=C`, all the constants and coefficients of the terms are integers, the terms have no common factors (besides 1), and the number in place of A is positive. Knowing this, convert the equation to standard form like so:

`y+1=(2)/(3) (x-8)\\y+1 = (2)/(3) x-(16)/(3) \\-(2)/(3) x+y+1 = -(16)/(3) \\-(2)/(3)x+y = -(16)/(3) -1\\-(2)/(3) x+y = -(16)/(3) -(3)/(3) \\-(2)/(3) x+y = -(19)/(3) \\2x-3y = 19`