Question

VERY SHORT ANSWER QUESTIONS
1
Find the angle between the lines y = 4 - 2x, y = 3x + 7.​

Answer 1

Answer:

45°

Explanation:

Data provided in the question:

y = 4 - 2x

y = 3x + 7

comparing with the general equation of line i.e y = mx + c

thus,

m₁ = -2

m₂ = 3

now,

tanθ = | m₁ - m₂ | ÷ | 1 + m₁ × m₂ |

here,

θ is the angle between the lines

Thus,

tanθ = | -2 - 3 | ÷ | 1 + (-2 × 3 ) |

or

tanθ = | -5 | ÷ | 1 - 6 |

or

tanθ = 5 ÷ 5

or

tanθ = 1

or

θ = 45°                 [as tan(45°) = 1 ]

Answer 2

Angle between line will be 45°

Explanation:

We have given two equations of line $y=4-2x$ and $y=3x+7$

We know the standard equation of line is $y=mx+c$, here m is alope and c is intercept

On comparing first line equation with standard equation $m_1=-2$

And on comparing second equation of line with standard equation $m_2=3$

Angle between two lines is given by

$tan\Theta =\frac{m_1-m_2}{1+m_1m_2}=\frac{-2-3}{1+(-2)\times (3)}=-1$

$\Theta =tan^{-1}(1)=-45^{\circ}$

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