slope-intercept form of the equation

Question

write the slope-intercept form of the equation of the line passing through (4, -1) and (6-7)

Answer 1

The slope intercept equation is

 

Y = mX + b

 where m is the slope.

 

m = (Y₂ - Y₁)/(X₂ - X₁)

 

Using the coordinates we have, we can solve m. The coordinates are (4, -1) and (6-7)

Y₁ = -1

Y₂ = -7

X₁ = 4

X₂ = 6

 

m = (-7 - -1)/(6 - 4)

     = (-7+1)/2

     = -6/2

     = -3

 

So back to our slope equation, Y = mX + b

 

We have m now. So we substitute X₁ and Y₁ in the equations as well so we can solve for b.

 

Y = mX + b

-1 = -3(4) + b

-1 = -12 + b

-1+12 = b

11 = b

 

So we have b. 

 

The final version of the equation is therefore:

 

Y = mX + b

Y = -3X + 11