(A) Let $L_1 \equiv 2x + 3y - 7 = 0$ and $L_2 \equiv 2x + 3y - 5 = 0$. The slope of a line $ax + by + c = 0$ is given by $m = -\frac{a}{b}$. For $L_1$

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(A) Let $L_1 \equiv 2x + 3y - 7 = 0$ and $L_2 \equiv 2x + 3y - 5 = 0$. The slope of a line $ax + by + c = 0$ is given by $m = -\frac{a}{b}$. For $L_1$,the slope $m_1 = -\frac{2}{3}$. For $L_2$,the slope $m_2 = -\frac{2}{3}$. Since $m_1 = m_2$,the lines have the same slope but different intercepts,therefore they are parallel to each other.

Class 11 Mathematics Straight Line Angle between two straight lines

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To which of the following types do the straight lines represented by $2x + 3y - 7 = 0$ and $2x + 3y - 5 = 0$ belong?

A
Parallel to each other
B
Perpendicular to each other
C
Inclined at $45^{\circ}$ to each other
D
Coincident pair of straight lines

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Straight Line

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Angle between two straight lines

If the lines $y = (2 + \sqrt{3})x + 4$ and $y = kx + 6$ are inclined at an angle of $60^{\circ}$ to each other,then the value of $k$ will be

Easy

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MediumTS EAMCET 2019

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The distance of a point $(2, 5)$ from the line $3x + y + 4 = 0$ measured along the lines $L_1$ and $L_2$ are the same. If the slope of line $L_1$ is $\frac{3}{4}$,then the slope of the line $L_2$ is

MediumMHT CET 2023

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$A$ line $L$ passes through the point $(3, -2)$ and is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x + y = 1$. If $L$ also intersects the $x$-axis,then the equation of $L$ is:

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To which of the following types do the straight lines represented by $2x + 3y - 7 = 0$ and $2x + 3y - 5 = 0$ belong?

Similar Questions

If the lines $y = (2 + \sqrt{3})x + 4$ and $y = kx + 6$ are inclined at an angle of $60^{\circ}$ to each other,then the value of $k$ will be

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines which make an angle of $30^{\circ}$ with the line joining the points $(1, 2)$ and $(3, 4)$,then $\frac{m_1}{m_2} = $

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