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: