Pre-Calc Question

Question

Which of the following is the equation of a line perpendicular to the line y = -10x + 1, passing through the point (5,7)?
1/10x-y=-13/12
1/10x+y=-13/2
1/10x+y=-13/2
-1/10x-y=13/2

Answer 1

a line perpendicular to y=-10x+1 will have a slope that is the negative reciprocal of -10

the negative reciprocal of -10 is 1/10, so m=1/10

y=(1/10)x+b so far

the line goes through the point (5,7)

using the point-slope form

y-y₁=(1/10)(x-x₁) where (x₁,y₁)=(5,7)

y-7=(1/10)(x-5)

y-7=(1/10)x-(1/10)(5)

y-7=(1/10)x-(5/10)

y=(1/10)x+7-(1/2)

y=(1/10)x+(6 1/2)

y=(1/10)x+(13/2)

rearranging terms...

(-13/2)=(1/10)x-y, the first answer

you should notice that in the standard form, y and (1/10)x are on different sides of the equation

if you put them on the same side of the equation, one term will have a positive sign and one term will have a negative sign

look at the answer choices...

the last three answers have both terms with the same sign which is incorrect so you could have eliminated them right away