ALEKS BLUE Writing the equation of a line through two given points
I THINK what you are asking is how to write an equation if you are given two points. To
do this (1) find the slope and (2) find the y-intercept.
To find the slope:
1. Start with one of the points, it doesn't matter which one, and write the ycoordinate on the top and the x-coordinate on the bottom.
2. Then subtract on both the top and bottom
3. Finally, write the y-coordinate of the second point on the top and the x-coordinate
of the second point on the bottom. It's best to put the second points in
parenthesis.
4. Simplify this and you'll have the slope.
Now that we know the slope, we know part of the equation:
Now that you have the slope, you need to find the y-intercept (the value of b). To find
the value of b, pick one of the original points (again, it doesn’t matter which one
because both points are on the line and are solutions for the equation).
I’ll choose the point (1, -8)
3
x b
4
Use the point 1, 8  and solve for b:
y 
3
1   b
4
3
8    b
4
Multiply both sides by 4 to eliminate the fraction:
8  
 3
4  8   4     4 b 
 4
32  3  4b
Add 3 to both sides:
29  4b
Divide both sides by 4 to isolate (solve) for b:

29
b
4
Now that you know what the slope (m) is and what the y-intercept (b) is,
you can write the equation:
y 
3
29
x 
4
4