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Answer 1

$\large\underline{\sf{Solution-1}}$

The standard form of the equation of line is Ax + By = C

$\rm\implies \:1 \:\longmapsto\: \: E$

$\large\underline{\sf{Solution-2}}$

The slope intercept form of the equation of line is y = mx + b

$\rm\implies \:2 \:\longmapsto\: \: G$

$\large\underline{\sf{Solution-3}}$

We know, Equation of line having slope m and y - intercept b units is y = mx + b

Given that,

Slope of line, m = - 1

Intercept on y - axis, b = 11

So, equation of line is

$\rm\implies \:y = - x + 11$

$\rm\implies \:3 \:\longmapsto\: \: F$

$\large\underline{\sf{Solution-4}}$

Given that,

Slope of line, m = - 2

Intercept on y - axis, b = 5

So, equation of line is

$\rm\implies \:y = - 2x +5$

$\rm\implies \:4 \:\longmapsto\: \: H$

$\large\underline{\sf{Solution-5}}$

We know, Equation of line which passes through the point (a, b) having slope m is y - b = m(x - a)

Given that

Slope of line is 3 and passes through the point (0, 9),

So, equation of line is

$\rm \: y - 9 = 3(x - 0)$

$\rm \: y - 9 = 3x$

$\rm\implies \:\rm \: y = 3x + 9$

$\rm\implies \:5 \:\longmapsto\: \: D$

$\large\underline{\sf{Solution-6}}$

We know,

Equation of line which makes an intercept of a and b units respectively on x - axis and y - axis is x/a + y/b = 1

Given that,

Intercept on x - axis, a = 2

Intercept on y - axis, b = 4

So, equation of line is

$\rm \: \dfrac{x}{2} + \dfrac{y}{4} = 1$

$\rm \: \dfrac{2x + y}{4} = 1$

$\rm\implies \:2x + y = 4$

$\rm\implies \:y = - 2x + 4$

$\rm\implies \:6 \:\longmapsto\: \: C$

$\large\underline{\sf{Solution-7}}$

Given that,

Slope of line is 3/2 and passes through the point (0, - 1)

So, equation of line using Slope point form is

$\rm \: y + 1 = \dfrac{3}{2}(x - 0)$

$\rm \: 2y + 2 = 3x$

$\rm\implies \:3x - 2y = 2$

$\rm\implies \:7 \:\longmapsto\: \: J$

$\large\underline{\sf{Solution-8}}$

Given that,

Intercept on x - axis, a = 5

Intercept on y - axis, b = 2

So, equation of line is

$\rm \: \dfrac{x}{5} + \dfrac{y}{2} = 1$

$\rm \: \dfrac{2x + 5y}{10} = 1$

$\rm\implies \:2x + 5y = 10$

$\rm\implies \:8 \:\longmapsto\: \: B$

$\large\underline{\sf{Solution-9}}$

Intercept on x - axis, a = 2/3

Intercept on y - axis, b = 3/2 in negative direction of y - axis

So, equation of line is

$\rm \: \dfrac{3x}{2} - \dfrac{2y}{3} = 1$

$\rm \: \dfrac{9x - 4y}{6} = 1$

$\rm\implies \:9x - 4y = 6$

$\rm\implies \:9 \:\longmapsto\: \: A$

$\large\underline{\sf{Solution-10}}$

Intercept on x - axis, a = 4 in the negative direction of x- axis

Intercept on y - axis, b = 5

So, equation of line is

$\rm \: - \dfrac{x}{4} + \dfrac{y}{5} = 1$

$\rm \: \dfrac{ - 5x + 4y}{20} = 1$

$\rm \: - 5x + 4y = 20$

$\rm\implies \:\rm \: 5x - 4y + 20 = 0$

$\rm\implies \:10 \:\longmapsto\: \: I$

Answer 2

Question (1) :

The Standard form of Equation of Line is given by Ax + By = C

∴ option (E) is the Answer.

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Question (2) :

Slope-intercept form of Equation of Line is Given by y = mx + c

∴ option (G) is the Answer.

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Question (3) :

Slope = -1

Points = (0,11) , y coordinate is 11

on substituting in y = mx + b

Equation of Line :

➻ y = -x + 11

∴ option (F) is the Answer.

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Question (4) :

slope (m) = -2

b = 5

on substituting in y = mx + c

Equation of Line :

➻ y = -2x + 5

∴ option (H) is the Answer.

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Question (5) :

slope = 3

points = (a,b) = (0,9)

by using y - b = m(x - a)

➻ y - 9 = 3(x - 0)

➻ y - 9 = 3x

➻ y = 3x + 9

∴ option (D) is the Answer.

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Question (6) :

a = 2 , b = 4

by using,

$\pink{ \rm\frac{x}{a} + \frac{y}{b} = 1}$

so, Equation of Line :

$\rm \frac{x}{2} + \frac{y}{4} = 1$

$\rm \frac{2x + y}{4} = 1$

$\rm y = 4 - 2x$

∴ option(C) is the Answer.

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Question (7) :

slope = 3/2

(a,b) = (0,-1)

by using, y - b = m(x - a)

Equation of Line :

➻ y + 1 = 3/2(x - 0)

➻ y + 1 = (3/2)x

➻ 2y + 2 = 3x

➻ 3x - 2y = 2

∴ option(J) is the Answer.

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Question (8) :

a = 5 , b = 2

so, by using

$\rm \frac{x}{a} + \frac{y}{b} = 1$

so,

$\rm \frac{x}{5} + \frac{y}{2} = 1$

$\rm \frac{2x + 5y}{10} = 1$

2x + 5y = 10

∴ option (B) is the Answer.

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Question (9) :

a = 2/3 , b = -3/2 it is in negative direction

formula we have to use is

$\red{ \rm \frac{x}{a } - \frac{y}{b} = 1}$

so,

$\rm \frac{3x}{2} - \frac{2y}{3} = 1$

$\rm 9x - 4y = 6$

∴ option (A) is the Answer.

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Question (10) :

b = 5 , a = -4 it is in negative direction.

formula we have to use is

$\purple{ \rm \frac{ - x}{a} + \frac{y}{b} = 1}$

so,

$\rm \frac{ - x}{4} + \frac{y}{5} = 1$

$\rm 4y - 5x = 20$

$\rm 5x - 4y + 20 = 0$

∴ option(I) is the Answer.

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$\underline{ \color{green} \rm FINAL \: \: ANSWERS \: } :$

1 ➻ E

2 ➻ G

3 ➻ F

4 ➻ H

5 ➻ D

6 ➻ C

7 ➻ J

8 ➻ B

9 ➻ A

10 ➻ I

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