1. ## Find the equation

...of a straight line that passes through the points (1,5) and (7, -1).

Here's my answer, is this correct? or is their an easier method?

Y1 - Y2 / X1 - X2
5 - (-1) / 1 - 7
6 / -6
Knowing the formula y=mx+b and m slope to be = -1 , we can plug back in:
5 = (-1) 1 + b
5 = -1 + b
5 - (-1) = b
6 = b
y = (-1)x + b

2. Nearly there, your value for m is correct, however you then need to find an actual value for b.

If we look at the first point, when x =5, y=1, putting this into our equation for the line we get the following:

$1 = -5 + b$

Solving this will give you the value for b

3. Just a quick note, it does not matter which coordinate you choose to use, (1,5) or (7, -1), they will both give you the same answer for b

Hope this helps

Craig

4. b = 6

have i explained it clearly?

5. y = (-1)x + 6

?

6. I am sorry you are quite right, did not see that last bit of your question.

Yes you are correct, and that is the best way in my opinion.

7. Ok great,

so the original post all makes sense?

8. Yep all makes sense

...of a straight line that passes through the points (1,5) and (7, -1).

Here's my answer, is this correct? or is their an easier method?

Y1 - Y2 / X1 - X2
5 - (-1) / 1 - 7
6 / -6
=(-1)
Knowing the formula y=mx+b and m slope to be = -1 , we can plug back in:

y=(-1)x+b

knowing that (1,5) is a point on the line. we put this in the equation to determine "b"

5 = (-1) 1 + b
5 = -1 + b
5 - (-1) = b
6 = b

Hence the answer that we get is

y = -x + 6

Correct!!

Everything in your answer is correct. But as you can see by Craig's replies that your presentation needs improvement...I am sure you will try to explain it a bit better next time. A bit of addition in red

10. "Hence the answer that we get is

y = -x + 6"

shouldnt it be this?

y = (-1)x + b

11. No.

(-1)x is the same as -x, mine and Ardash's version is easier to read and help avoid possible confusion.

Also you wanted the equation of the line, this is the equation in it's numerical form, not with a 'b' still in it.

"Hence the answer that we get is

y = -x + 6"

shouldnt it be this?

y = (-1)x + b
..... than tell me why have you found the value of b as 6 ?

The steps that you followed were

1-Assume the equation as

y= mx+b
where m and b are initially unknown constants

2-Find m

3-Find b

4-Put the values that you found for them

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EDIT: