Intercepts of a Line
If a line cuts x – axis at A (a, 0) and y – axis at B (0, b), then a is called x – intercepts and b is called y – intercepts of the line.

Examples:
- If a line cuts x – axis at (2, 0), then x – intercept is 2
- If a line cuts y – axis at (0, 3), then y – intercept is 3
Slope Intercept Form:
Theorem: The equation of the line having slope m and y – intercept c is y = mx + c.
Proof:
y – intercept of the line is c, the line cuts y – axis at (0, c)
we know that
(y – y₁) = m (x – x₁)
(x₁, y₁) = (0, c)
(y – c) = m (x – 0)
y – c = mx
y = mx + c
Example: find the equation of the line having inclination 45° and y intercept 3
Solution:
Slope =m = tan45° =1
The equation of the line having slope m and y – intercept c is y = mx + c
y = (1)x + 3
y = x + 3