Question

The slope of the line which makes 3 pie ÷ 4 with the +ve direction of x axis is​

Answer 1

Answer:

Slope of the line is - 1

Step-by-step explanation:

Given,

Angle of line from positive direction of x- axis Ф = 3π/4

∵ Slope of any line will be tangent of angle of line from positive direction of x- axis.

slope = tanФ

so slope = tan3π/4

= tan (π + π/4)

∵ tan (π + ∅) = - tan∅

= - tan(π/4)

= - 1

So slope of the line is - 1

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Answer 2

Answer:

The slope of the line is $-1$.

Step-by-step explanation:

Concept:-

• Slope of a line = tanα, where α is the inclination of the angle.
• Recall the identity, tan(A - B) = $\frac{tanA-tanB}{1+tanAtanB}$

Step 1 of 1

Given:-

A line makes an angle with the positive direction of x-axis is $\frac{3\pi}{4}$, i.e.,

Inclination of the angle, α = $\frac{3\pi}{4}$

To find:-

The slope of the line.

As we know,

Slope of a line is,

= tanα

= tan$\left(\frac{3\pi}{4}\right)$

= tan$\left(\pi-\frac{\pi}{4}\right)$

Using the identity, we have

= $\frac{tan\pi-tan(\pi/4)}{1+tan\pi tan(\pi/4)}$

= $\frac{0-1}{1+0(1)}$  (Since tan$\pi$ = 0 and tan$(\pi/4)$ = 1)

= -1

Final answer: The slope of the line is $-1$.

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