To find the y-intercept of a line, substitute the values of x and y coordinates into an equation representing the line. Set x to 0, then solve for y. If the equation is already in the slope-intercept form of y = mx + b, the value of b is the y-intercept.
- Write the equation of the line in standard form
The standard form of a linear equation is ax + by = c. The variables a and b are coefficients of x and y ordered pairs.
- Substitute 0 for the value of x
The y-intercept is the point of a line that lies on the y-axis, so x has to be 0. For example, if the equation 3x + 5y = 15 is present, you substitute 0 for x, so you only have to solve for y.
- Solve for y
Divide both sides of the equation by the coefficient of y. Using the example, this would be 5, leaving y as 3.
- Plug both values into the original equation to see if it holds true
The equation should look like 3(0) + 5(3) =15. Because the two sides are equal, the point (0, 3) lies on the line represented by 3x + 5y = 15.