# Slope Intercept Form

## Workout Examples

Example 1: Find the equation of a straight line making an angle of 60° with the x-axis and cutting an intercept 3 from the y-axis.

Solution: Here,

Θ = 60°

y-intercept (c) = 3

slope (m) = tan60° = √3

The equation of the line is,

y = mx + c

i.e.       y = √3x + 3

The required equation of the line is y = √3x + 3.

Example 2: Find the equation of a straight line which is inclined to the x-axis at an angle 30° and cutting an intercept 2 from y-axis.

Solution: Here,

Θ = 30°

y-intercept (c) = 2

slope (m) = tan30° = 1/√3

The equation of the line is,

y = mx + c

i.e.       y = (1/√3)x + 2

or,        y = (x + 2√3)/√3

or,        x + 2√3 = √3y

or,        x  - √3y + 2√3 = 0

The required equation of the line is x - √3y + 2√3 = 0.

Example 3: Find the equation of straight line passing through the points (0, -2) and (2, 1).

Solution: Here,

The straight line passes through the points (0, -2) and (2, 1).

slope (m) = (y2 – y1)/(x2 – x1)

= (1 + 2)/(2 – 0)

= 3/2

The point (0, -2) is on y-axis.

y-intercept (c) = –2

The equation of the straight line is,

y = mx + c

i.e.       y = (3/2)x – 2

or,        y = (3x – 4)/2

or,        3x – 4 = 2y

or,        3x  2y – 4 = 0

The required equation of the line is 3x  2y – 4 = 0.

You can comment your questions or problems regarding slope intercept form of the equation here.