find the inclination angle

Question

Find the inclination (in radians and degrees) of the line passing through the points.

(6,1)(10,8)

Answer 1

The slope - intercept form is y = mx + b, m is slope and b is y-intercept

The given points are (6,1)(10,8)

Slope formula (m) = (y₂-y₁)/(x₂-x₁)

Substitute the values in slope formula

= (8 -1)⁄(10 -6)                                                    ((x₁,y₁)= (6, 1)and(x₂,y₂) = (10, 8))

There fore slope(m) = 7⁄ 4                                (Simplify )

The slope intercept form is y = (7/4) x + b

Slope = 7/4

m =  7/4

Re call m = tanθ, where θ is inclination angle

m = tanθ =7/4

tanθ = 1.75                                                (7/4 = 1.75)

tanθ = 60.25^o                   

θ = 60.25^o and 60.25^o × Π/180

θ = 60.25^o and 60.25^o × 3.14/180 (radians)       (Simplify)

θ = 60.25^o and 1.051 (radians)

Since the slope is positive Tangent sign should be positive, so the line passes through the I and II quadrant.

So, inclination angle is  60.25^o .