Give x a value of zero in the linear equation that describes the line.
For example, if the linear equation is 2x - y + 1 = 0, then substituting 0 for x gives you the equation 2(0) - y + 1 = 0 or -y + 1 = 0.
Isolate y on one side of the equation.
By subtracting 1 from both sides, you are left with the equation -y = -1.
Simplify the equation to solve for y. This is the value of the y-intercept.
The simplified equation is y = 1. Therefore, the line crosses the y axis at y = 1.
Select two points on the line. Name the coordinates of one point x1 and y1 and the coordinates of the second point x2 and y2.
For example, if a line has two points at (1,3) and (3,7), x1 = 1, x2 = 3, y1 = 3 and y2 = 7.
Substitute the coordinates into the slope formula, m = (y1 - y2) / (x1 - x2), where m equals the value of the slope of the line.
For instance, the slope of the line with points at (1,3) and (3,7) is determined by the equation m = (3 - 7) / (1 - 3).
Simplify the equation to determine the slope of the line.
The slope equation simplifies to m = -4/-2 or m = 2.
Substitute the value of the slope and the coordinates of one point into the slope-intercept formula, y = mx + b.
For instance, substituting the coordinates of the first point yields the equation 3 = 2(1) + b.
Solve the equation for b. This is the y-intercept.
Since 3 = 2 + b, b = 1. Therefore, the line crosses the y axis at y = 1.