Question

if Slope of a line is 1 then angle of inclination of that degree is?
a:0 b:45 c:90 d:135​

Answer 1

Required Answer:-

Slope is the inclination of anything or we can say that it is the ratio between the vertical rise and horizontal distance from a certain point.

This ratio is also known as Tangent (tan Θ). The slope of a straight line is the tangent of its inclination and is denoted by letter ‘m’ i.e. if the inclination of a line is θ, its slope m = tan θ$.$

GiveN:-

• Slope (tan Θ) = 1

And we need to determine the value of Θ?

We know that, In trigonometry tan Θ is 1 when Θ = 45° because sin 45° and cos 45° is same in value.

Hence:-

• The angle of inclination Θ = 45° (Option B)

Explore more:-

• Slope is very helpful in finding the equation of straight line when y-intercept (c) is also given.

• Slope = Difference in y-coordinates / Difference in x-coordinates.

Answer 2

Given :-

• θ is the inclination of a straight line, then tanθ is called the slope of a line.

• The slope of a line is usually denoted by m.

 Solution:-

• Here, it is given that the slope of the line is m=1, therefore, the angle of inclination is:

$\bold{m \: = tan \theta}\\ \\ \bold{1 \: = tan \theta}\\ \\ \bold{tan \:45 \degree = tan \theta}\\ \\ \bold{ \theta \: = 45 \degree}$

Hence, the correct option is 45⁰..