What is the equation of the line passing through (0, 2) and perpendicular to the line y = 4x – 3 in slope-intercept form?

y = negative one-fourthx + 2

y = one-fourthx + 2

y = 4x + 2

y = –4x + 3

Question

What is the equation of the line passing through (0, 2) and perpendicular to the line y = 4x – 3 in slope-intercept form?

y = negative one-fourthx + 2

y = one-fourthx + 2

y = 4x + 2

y = –4x + 3

anonymous · Answer

do you any clues on how to solve it?

anonymous · Answer

not really

anonymous · Answer

ok so the first thing we need to notice is that they give us one point (0,2) and its perpendicular to the line of y = 4x +3.
so to find the equation of the other line we will have to use the point given (0,2) and also find something else to help us get to the final answer, and it is the gradient/slope.

anonymous · Answer

They tell us its perpendicular, this means that m1 x m2 = -1
m1=gradient one     
m2=gradient two

from the equation y = 4x + 3
what is the gradient equal to?

anonymous · Answer

im not sure

anonymous · Answer

ok, you have to remember this.

anonymous · Answer

For the equation y = 4x + 3 and any other equation rearranged in the form y = ax + c 
the gradient/slope represented by the symbol m is equal to whatever is in front of the x, in this case it is 4.

anonymous · Answer

y = 4x + 3
m(gradient/slope)= 4

anonymous · Answer

got it?

anonymous · Answer

yes. i understand now

anonymous · Answer

ok, good.

anonymous · Answer

lets try one quick example first, so what would the gradient of y=10x + 2 be?

anonymous · Answer

10

anonymous · Answer

yes, that's great.

anonymous · Answer

so the answer is c? right?

anonymous · Answer

nope.

anonymous · Answer

a*?

anonymous · Answer

ok, I am not going to tell you the answer yet as guessing is not the right way to understanding.

anonymous · Answer

so we have one point given (0,2) and the unknown line has to be perpendicular to the line of y=4x + 3.

m1=gradient of first line (this is known from y=4x + 3, which is 4)
m2=gradient of second line (unknown)
m1 x m2 = -1
   4 x m2 = -1
         m2 = -1/4

y=mx + c
y= -1/4x + c
(0,2)   2=-1/4(0) + c
          2= 0 + c
          c = 2

therefore the answer is y=-1/4x + 2 which is answer A.

anonymous · Answer

it all makes sense now. ill make sure to remember this next time. Thanks @JayDS

anonymous · Answer

your welcome, I just want to make sure you really understand it.

anonymous · Answer

i appriciate that. i understand now. thanks again!