What is the Y=mx+b, given these conditions: passes through (5,4) and (-1,2)?

Question

Please show work too

Answer 1

Y=mX+b

Y-mX-b=0 ------(1)

if it passes through

(5,4) must satisfy the equation

so take x=5, y=4 and substitute in equation (1)

so  4 - 5m-b=0

5m+b=4 ........ (2)  

the point (-1,2) also satisfies the equation so

x=-1, y=2 for equation gives -

2-(-1)m-b=0

m-b=-2.....(3)  

solving equations (2) and  (3)  

from equation (2)  

b=4-5m

substitute b value in equation (3)

so m-(4-5m)= -2

m-4+5m = -2

6m=-2+4=2

m= 1/3  

m-b= -2

so  1/3-b = -2

b=1/3+2 =5/3

so the equation is

Y=(1/3)X+ (5/3)

X+5=3Y

X-3Y+5=0   is the desired equation  

Answer 2

There are two major ways to approach the problem. The previous replies involved finding the slope m.

Possibly you might want to look at this alternate way of doing the problem:

y = mx + b

Substitute each pair of coordinates getting these two equations.

4 = 5m +b

2 = -1m +b

Subtracting to cancel the constant b we get:

2 = 6m

m= 1/3

Substituting to solve for b we get:

4 = 5*1/3 + b

4 = 5/3 + b

12/3 - 5/3 = b

b = 7/3

Your answer is:

y = 1/3*x + 7/3

Answer 3

(y-4)/(x-5) = (2-4)/(-1-5)

Simplify and you'll get what you want.

Answer 4

m = 1/3

y = (1/3) x + 7/3

Answer 5

m = (2 - 4) / (-1 - 5)

m = - 2 / - 6

m = 1/3

y - 4 = (1/3) (x - 5)

y = (1/3) x - 5/3 + 12 /3

y = (1/3) x + 7/3

Answer 6

First find the slope...

m = (2 - 4) / (-1 - 5) = -2/-6 = 1/3

Then find "b" (the y-intercept)...

b = y1 - m*x1 = 4 -(1/3)(5) = 7/3

y = (1/3)*x + 7/3

Take care,

David

www.tutor-homework.com

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Answer 7

m = (2 - 4)/(-1 - 5)

m = -2/-6

m = 1/3

using formula:-

y - y1 = m(x - x1)

when at point (5 , 4);

y - 4 = 1/3(x - 5)

y - 4 = (x - 5)/3

3(y - 4) = x - 5

3y - 12 = x - 5

3y = x - 5 + 12

3y = x + 7

x = 1/3x + 7/3