Find the equation of the line in slope intercept form which will pass through the points (2,3) and (4,-2).

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mwmovr40 | College Teacher | (Level 1) Associate Educator

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To be in slope-intercept form the equation must fit

 

We have two unknowns (m and b) so we need to plug in our given points and solve for the unknowns.

``

`` If we subtract the bottom equation from the top we get

`` so  `m = -5/2` plugging this into the first equation we get

`3 = -5/2*2 + b` which shows us that b = 8

Checking in the second equation we see `-5/2*4 + 8 = -2`

The equation of the line must be

`y = -5/2x + 8`

 

Alternate solution:

to get the slope

`m = (y_2-y_1)/(x_2-x_1) = (-2-3)/(4-2) = -5/2`

 

substituting this into the slope intercept equation along with `(x_1,y_1)` we get

`3 = -5/2*2 + b = -5 + b` so again b = 8  and the equation is

`y = -5/2x + 8`

 

 

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