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Which of the following is a point-slope equation of a line that passes through

the points (5,2) and (-1,-6)?
A. y-2-(X-5)
B. y-2-(X-5)
C. y-2 =(x-5
D. V-2--0-5)

1 Answer

1 vote

Please, check the options of the question. The point-slope equation needs the slope, m, in the equation.

Answer:

The point-slope equation of the points (5,2) and (-1,-6) is


\\ y - 2 = (4)/(3)(x-5) or,


\\ y + 6 = (4)/(3)(x+1)

which are the same as


\\ 3y-4x+14 = 0 , (which is not a point-slope equation, though)

Explanation:

The point-slope equation is given by:


\\ y - y_(1) = m(x - x_(1))

Where m is the slope of the line:


\\ m = (y_(2) - y_(1))/(x_(2) - x_(1))

Having the points (5,2) and (-1,-6), then


\\ m = (-6 - 2)/(-1 -5)


\\ m = (-8)/(-6)


\\ m = (4)/(3)

Then, the point-slope equation of the points (5,2) and (-1,-6) is


\\ y - 2 = (4)/(3)(x-5) or


\\ y + 6 = (4)/(3)(x+1)

The below graph represents both lines (they are the same line).

Which of the following is a point-slope equation of a line that passes through the-example-1
User Artem Razin
by
8.4k points

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