What is the equation of a line that satisfies the given conditions: perpendicular to #y= -2x + 5# and passing through (4, -10)?

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Answer 1 · 2015-12-06T19:55:24

#y=1/2x-12#

Perpendicular lines have opposite reciprocal slopes.

The slope of the line #y=-2x+5# is #-2#.

The opposite reciprocal of #-2# is #1/2#, which is the slope of the perpendicular line.

We also know that the line passes through the point #(4,-10)#.

We can use the #y=mx+b# form of the line to determine the equation.

We know that:
#x=4#
#y=-10#
#m=1/2#
And we want to solve for #b#.

#-10=1/2(4)+b#

#-10=2+b#

#-12=b#

The equation of the line is #y=1/2x-12#.