Write the education of a line that passes through (3,1) and is perpendicular to the line y=-3x +2

Question

This is a question i need help answers please.

Answer 1

We're given a point, so we're going to need the point-slope formula:

y - y₁ = m(x - x₁)

Now we need the slope. Forming a perpendicular line means that we need to take the negative inverse of the original line's slope, that is, flip the numerator and denominator and multiply by -1:

-3 → ¹/₃

When we add in the ordered pair (3, 1), that gives us the following:

y - 1 = ¹/₃(x - 3)

 

From here you should be able to isolate y on your own.

Answer 2

I am sure you meant to to say "equation of a line", not "education of a line", right?  Its slope is the negative reciprocal of the slope of the given line, so

 

m = -1/(-3) = 1/3

 

y = (1/3)x + b

 

Use the point (3,1) to find b.

 

1 = (1/3)(3) + b

 

1 = 1 + b

 

b = 0

 

y = (1/3)x

Answer 3

This will take little time at all. The key lies in understanding that Perpendicular lines must be as opposite as possible. They do that by making their slopes as different as they can get. In other words, upside down and backwards. The old slope was:

m = -3

...so the new slope will be the reciprocal with the opposite sign:

m = -1 / -3  = 1/3

Now we have the slope, but we still require the y-intercept, b

To get that, use the only equation containing it:

Y = mX + b

Plug in everything we know:

1 = (1/3) * 3 + b

The fraction cancels our x...

1 = 1 + b

-1   -1

0 = b

Your final equation is:

Y = (1/3) X + 0

or simply

Y = (1/3) X