If the angle between two lines is π 4 and slope of one of the lines is 1 2 , find the slope of the other line.

We know that the acute angle θ between two lines with slopes m 1 and m 2 is given by tan θ = m 2 - m 1 1 + m 1 m 2 . . . 1 Let m 1 = 1 2 , m 2 = m and θ = π 4 . Now, putting these values in 1 , we get tan π 4 = m - 1 2 1 + 1 2 m ⇒ 1 = m - 1 2 1 + 1 2 m Now, m - 1 2 1 + 1 2 m = 1 or m - 1 2 1 + 1 2 m = - 1 . ⇒ 2 m - 1 2 = 2 + m 2 or 2 m - 1 2 = - 2 + m 2 ⇒ m = 3 or m = - 1 3 Figure below explains the reason of two answers. Hence, slope of the other line is 3 or - 1 3 .

If the angle between two lines is π 4 and slope of one of the lines is 1 2 , find the slope of the other line.

We know that the acute angle θ between two lines with slopes m 1 and m 2 is given by tan θ = m 2 - m 1 1 + m 1 m 2 . . . 1 Let m 1 = 1 2 , m 2 = m and θ = π 4 . Now, putting these values in 1 , we get tan π 4 = m - 1 2 1 + 1 2 m ⇒ 1 = m - 1 2 1 + 1 2 m Now, m - 1 2 1 + 1 2 m = 1 or m - 1 2 1 + 1 2 m = - 1 . ⇒ 2 m - 1 2 = 2 + m 2 or 2 m - 1 2 = - 2 + m 2 ⇒ m = 3 or m = - 1 3 Figure below explains the reason of two answers. Hence, slope of the other line is 3 or - 1 3 .

Find the equation of straight line whose slope is 10 3 and passes through the point 0 , 5 .

Given: Slope m = 10 3 Co-ordinates of point x 1 , y 1 = 0 , 5 We know that, y - y 1 = m x - x 1 y - 5 = 10 3 x - 0 3 y - 15 = 10 x - 0 10 x - 3 y + 15 = 0 Hence, the equation of straight line is 10 x - 3 y + 15 = 0 .

Find the equation the straight line whose slope is 2 3 and passing through 5 , - 4 .

Given: Slope of line m = 2 3 and line passes through 5 , - 4 Slope of line m = y 2 - y 1 x 2 - x 1 Here, x 1 = 5 y 1 = - 4 x 2 = x coordinate of another point is x y 2 = y coordinate of another point is y Putting the values in the slope formula, ⇒ 2 3 = y - - 4 x - 5 ⇒ 2 x - 5 = 3 y + 4 ⇒ 2 x - 10 = 3 y + 12 ⇒ 2 x - 3 y - 22 = 0 Hence, the equation is 2 x - 3 y - 22 = 0

HARD

Earn 100

If the angle between two lines is $\frac{π}{4}$ and slope of one of the lines is $\frac{1}{2}$ , find the slope of the other line.

Important Questions on Straight Lines

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

Find the equation of straight line whose slope is

\frac{10}{3}

and passes through the point

(0, 5)

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

A straight line with negative slope passing through

(1, 1)

cuts the

x

-axis at

A

and

y

-axis at

B

, where

O

is the origin. If

θ = ∠ O A B

, then the area of the triangle

O A B

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

The vertices of a

△ A B C

are

A (3, 8), B (- 1, 2)

and

C (6, - 6)

. Find slope of

B C

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

Find the equation of that straight line which passes through the points

(6, 0)

and whose slope is

\frac{7}{3}

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

Find the y-intercept of the line joining two points

(1, 3)

and

(3, 5)

HARD

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

A triangle has vertices at

(6, 7), (2, - 9)

and

(- 4, 1)

. Find the slope of its medians.

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

M

and

N

are two points on the

x

axis and

y

axis respectively.

P (3, 2)

divides the line segment

M N

in the ratio

2 : 3

. Find the slope of the line

M N

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

The points

(0, \frac{8}{3}), (1, 3), (82, 30)

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of X-axis is

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

If the tangent at the point

P

on the circle

x^{2} + y^{2} + 6 x + 6 y = 2

meets

the

straight

line

5 x - 2 y + 6 = 0

at a point

Q

on the

Y

-axis, then the length of

P Q

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

Slope of a line is

3

and

y

intercept is

- 4

. Write the equation of a line.

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

The points

(0, \frac{8}{3}), (1, 3)

and

(82, 30)

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

Slope of the straight line which is perpendicular to the straight line joining the points

(- 2, 6)

and

(4, 8)

is equal to:

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

A line passes through the points

(8, 5)

and

(10, 6)

, then find the slope of the line.

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

Find the equation the straight line whose slope is

\frac{2}{3}

and passing through

(5, - 4)

EASY

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

What is the slope of the line passing through the points $(5, 0)$ and $(3, 2)$ ? Write the equation of the line.

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

A student, while conducting an experiment on Ohm’s law, plotted the graph according to the given data. Find the slope of the line obtained.

$X$ -axis $I$	$1$	$2$	$3$	$4$
$Y$ -axis $V$	$2$	$4$	$6$	$8$

Question Image

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

α, β

are natural numbers such that

100^{α} - 199 β = (100) (100) + (99) (101) + (98) (102) + \dots . . + (1) (199),

then the slope of the line passing through

(α, β)

and origin is:

HARD

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

Let

O = (0, 0);

let

A

and

B

be points respectively on

x

-axis and

y

-axis such that

∠ O B A = 60 °

. Let

D

be a point in the first quadrant such that

O A D

is an equilateral triangle. Then the slope of

D B

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Slope of a Line

A rectangle is inscribed in a circle with a diameter lying along the line

3 y = x + 7 .

If the two adjacent vertices of the rectangle are

(- 8, 5)

and

(6, 5),

then the area of the rectangle

(

in sq. units

)

is:

If the angle between two lines is π4 and slope of one of the lines is 12, find the slope of the other line.

Important Questions on Straight Lines

Learn and Prepare for any exam you want !

If the angle between two lines is $\frac{π}{4}$ and slope of one of the lines is $\frac{1}{2}$ , find the slope of the other line.