write the equationof the line in slope intercept form with the given information

Question

(2,4) (5,-5)

I'm doing an easy a review and I don't remember how to do this type of problem. anything helps. thank you. :)

Answer 1

Slope intercept form of a line is y = mx + b  

 

If you are given 2 points on a line then the slope is the [Change in Y]/[Change in X].  This can also be called Delta-Y over Delta-X or Rise over Run.  For the points (2,4) and (5,-5) the slope is 

 

m = (-5 - 4) / (5 - 2) = -9/3 = -3  

 

Now that you know the slope, plug it into the equation y = mx + b along with one of the points (2,4) to determine what b is equal to  

 

4 = (-3)*2 + b

4 = -6 + b

b = 10  

 

So the equation of the line is  y = -3x + 10  

 

To check the answer, plug both of the given points in to the equation to make sure they are on the line 

 

-3*(2) + 10 = -6 + 10 = 4   Check for (2,4)

-3*(5) + 10 = -15 + 10 = -5  Check for (5,-5)