write the equation of the line perpendicular to y=-3x-5 that contains (3,4)

Question

I need help with this please.

Answer 1

Alright, Sunshine, this isn't as bad as it looks, I promise!

 

Our slope of the given line is -3.  A perpendicular line will have the opposite reciprocal, so the slope of our new line is 1/3.

 

Now, we take our new slope and our point and plug them into y = mx + b to find our y-intercept.

 

4 = 1/3(3) + b

4 = 1 + b

b = 3

 

We now have a slope of 1/3 and a y-intercept of 3, so our equation for the new line is y = (1/3)x + 3.

 

Let's check, using our point.

 

4 = (1/3)(3) + 3

4 = 1 + 3

4 = 4.  Check!

 

Hope this helps!

 

 

Answer 2

Hi Sunshine,

 

Lines that are perpendicular have slopes that are negative reciprocals.

 

the first line y =-3x -5 is in the form (y = mx + b   where m is the slope

 

So in this case the slope of the first line is

 

-3      and the negative reciprocal of -3 is 1/3

 

so our new line would be

 

y = 1/3x + b    and we can find b by putting the point (3,4) into the equation as follows

 

4 = 1/3(3)  + b

 

4 = 1 +  b

 

b = 3

 

so our equation of the new perpendicular line is

 

y = 1/3(x) + 3

 

Hope this helps