Question

Find an equation of the line containing the given pair of points
(3,4) and (9,6)

I got 2/3x+2. is this right?

Answer 1

The slope is (6-4)/(9-3) = (1/3)
y = (x/3) + constant
4 = (3/3) + constant
the constant = 3
y = (x/3) + 3

Your answer is not right. You could have verified that by substitution. You also need to insert parentheses into what you wrote because it is not clear if you mean
2/(3x) + 2, or 2/(3x+2) or (2/3)x + 2
All three are wrong.

Answer 2

Please clarify. what is constant?

Answer 3

How did you get 3. Did you subtract 1 from 4?

Answer 4

yes.
4-1 = 3 is the constant
I got it by forcing the line of slope (1/3) to go through the point (3,4)

I would have got the same answer by forcing it to go through the other point, (9,6).

Answer 5

okay i tried this one. is this right?

(2,4)and (6,7)

the slope is (7-4)/(6-2)=2/1
y=(x/1)+constant
4=(1/1)+constant
the constant=2
y=(x/2)+2

Answer 6

If the slope is 1/2, how can the equation be y = (x/1)+ 1?

Your very first line is wrong
(7-4)/(6-2) does not = 2/1 = 2
The slope is 3/4

The next line also makes no sense. Where did the x/1 come from?

For your new example, the slope is (3/4)
The equation must fit
y = mx + b where m = 3/4, x = 2 and y = 4
4 = (3/4)*2 + b
b = 5/2
y = (3/4)x + 5/2

Answer 7

how did you get 5/2?

Answer 8

I did the math

4 = (3/4)*2 + b

b = 4 - 3/2 = 5/2