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How to Build An Equation of A Line

In order to build the equation of the line you need the slope and one point (coordinate (X,Y), then you can use the equation Y=mX+b to find the equation of the line.


For example: Build the equation of the line that passes through point (2,5) with slope m=-3.


Step One: Substitute the slope and the coordinate given into the equation Y=mX+b

5= (-3)(2) +b


Step Two: Solve for b (also called the y-intercept):

5= -6+b
b= 11


Step Three: Now that you have the Y-intercept (or b) you can plug it back and build the equation in slope-intercept form.

Y= mX + b
Y=-3X+11


Let's do another example:


Build the equation of the line that passes through points (3,4) and (-2,5).


First we need to find the slope:


m= (Y2-Y1)/(X2-X1)= (5-4)/(-2-3) = 1/-5= -1/5


Now we can choose any coordinate (3,4) or (-2,5) (it does not matter you will get the same result because the line passes through both points, I am going to choose (3,4))


Let's build the equation with the information given:

m= -1/4
(3,4)


Y= mX+b
4= (-1/4)(3) + b
4= -3/4 + b
b= 4 + 3/4 = 15/4
Final answer:
Y= -1/4(x) +15/4


Practice Problems: