Question 1160030

an equation of the line passing through the point ({{{-2}}},{{{1}}}) and the perpendicular to the line {{{y=2x-5}}}

will be: use point-slope formula

{{{y-y[1]=m(x-x[1])}}} where {{{m}}} is a slope, {{{x[1]}}}and {{{y[1]}}} coordinates of given point

since this line is perpendicular to the line {{{y=2x-5}}} whose slope is {{{2}}}, your line will have a slope negative reciprocal which is {{{-1/2}}}

so 

{{{y-1=-(1/2)(x-(-2))}}}

{{{y-1=-(1/2)(x+2)}}}

{{{y-1=-(1/2)x-(1/2)(2)}}}

{{{y-1=-(1/2)x-1}}}

{{{y=-(1/2)x-1+1}}}

{{{y=-(1/2)x}}}-> your answer


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-2,1,.12),locate(-2,1,p(-2,1)),
 graph( 600, 600, -10, 10, -10, 10, 2x-5, -(1/2)x)) }}}