Locate two points on the first of the two lines that you want to calculate the slope for. These steps will refer to the coordinates 2,3 as the first point and 5,4 as the second point on the line. The first number in each coordinate is the X coordinate and the second is the Y coordinate for each point on the line. In this example, x1 = 2, x2 = 5, y1 = 3 and y2 = 4.
Insert the X and Y values into the formula m = y2 -- y1/ x2 -- x1. In this example, this formula would be expressed as 4 -- 3/ 5 -- 2.
Solve the formula m = 4 -- 3/ 5 -- 2. Simplified this would be m = 1/3. The slope for both this line and a line parallel to it will be 1/3 where 1 is the change in y and 3 is the change in x on a graph.
Insert the slope (m), y1 and x1 values in the formula y = mx + b. Use the previously established values y = 3, x = 2 and m = 1/3. The formula will look like 3 = 1/3(2) + b.
Solve the slope intercept form 3 = 2/3 + b. Simplify any fractions by multiplying the entire formula by the least common denominator of the fractions. Because the least common denominator in this formula is 3, the entire formula will be multiplied by 3 to look like this: 3(3) = 2/3(3) + b(3). Once the formula has been worked out it will be: 9 = 2 + 3b.
Isolate the y-intercept by subtracting the slope from both sides of the equation. 9 -2 = 2 + 3b -2. Once solved, the formula will appear as: 3b = 7. Because this example has yielded a multiple of b, the formula must be divided by that multiple to provide an accurate y-Intercept. The formula 3b/3 = 7/3 would simplify to b = 7/3.
Check the accuracy of the formula by adding in all of the information yielded from the previous steps. Because we have identified that y = 3, x = 2, m = 1/3 and b = 7/3, the slope intercept form would be 3 = 1/3(2) + 7/3. This works out to 3 = 2/3 + 7/3 which simplifies to 3 =9/3 or 3 = 3.
Repeat this process using the y1 and x1 coordinates of the parallel line to determine the y-intercept of the parallel line.