On a coordinate plane, a line goes through (1, negative 1) and (4, 2). A point is at (2, 5). What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y + 5 = x + 2 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)

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cooperbrown81 cooperbrown81 · Answer 1 · 2021-01-15T00:16:22+01:00

The equation is C. y − 5 = −(x − 2)

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ayoushivt ayoushivt · Answer 2 · 2022-07-21T07:13:38+02:00

The line equation is y − 5 = −(x − 2), and the correct option is C.

The equation of a straight line is given by

y = mx +c

where m is the slope and c is the y-intercept.

The line goes through the points (1, -1) and (4, 2),

The slope of the line will be

m = (y'-y)/(x'-x)

m = ( 2+1)/(4-1) = 1

The product of the slope of the line and the line perpendicular to it is -1

So, the slope of the line perpendicular to the given line is -1.

The line passes through the point (2,5)

The point-slope form is

(y-y') = m(x-x')

so, the equation will be

y − 5 = −(x − 2)

Therefore, the line equation is y − 5 = −(x − 2), and the correct option is C.

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