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:

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