how do i find y=mx+b from (9,8) and (7,3)

Question

im stuck please help me with this algebraic equation

Answer 1

Let P1=(x1,y1)=(9,8)

and P2=(x2,y2)=(7,3)

Where P1 and P2 are point 1 and 2 respectively.

 

then, m=(y2-y1)/(x2-x1)=(3-8)/(7-9)=-5/(-2)=5/2 :: this is your slope value, 

 

So finding b is, plugging P1 or P2 into y=mx+b to find b value, in this case let's use 

P2, x2 for x and y2 for y, to find b (just because it looks more simpler for plugging in the expression). 

y=mx+b becomes 3=(5/2)(7)+b then 3=(35/2)+b. By multiplying 2 on both sides we get 6=35+2b and subtracting 35 from both sides leads to 6-35=2b => -29=2b dividing both sides by two gives b=-29/2.

 

Therefore, your expression y=mx+b is y=(5/2)x+(-29/2), 

once again where m= 5/2 and b=-29/2. 

I hope this detailed methods helps you understanding the concept of 'finding an equation of the line that passes through 2 points (in this case the two points being (9,8) and (7,3))'

 

Thanks

 

Answer 2

First step: find 'm'

Second step: Use the 'm' with one of the coordinate pairs by substituting them into y = mx + b, to find 'b'

Third: Write y = mx + b with the values of 'm' and 'b'

 

m = (3 - 8)/(7 - 9) = - 5/- 2 = 5/2

y = mx + b

8 = (5/2)*9 + b

8 = 45/2 + b   or 16/2 = 45/2 + b

Subtract 45/2 from each side

- 29/2 = b

b = - 29/2

y = mx + b

y = (5/2)x - 29/2

 

Hope it helped, Jim.

Mary Ann

Answer 3

Easy. Slope = m = delta y/delta x =( 8 -3)/(9 - 7) = 5/2

 

y = 5/2 x + b

 

to solve for b plug in one of the coordinates

 

8 = 5/2 * 9 + b

 

b = 8 - 45/2 = 8 - 22.5 = -14.5

 

y = 5/2 * x - 14.5

 or

y = 5/2 x - 29/2

 

or 

 

2y = 5x - 29

 

or 

 

5x - 2y = 29