1 Marks Question

Question 11 Mark

From the choices given below, choose the equation whose graph is given in Fig.

y = x + 2
y = x - 2
y = -x + 2
x = 2y = 6

[Hint: Clearly (2, 0) and (-1, 3) satisfy the equation y = -x + 2]

Answer

Clearly (2, 0) and (-1, 3) satisfy the equation y = -x + 2.
$\therefore$ The equation whose graph is given is y = -x + 2.

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Question 21 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
$\text{y}=\frac{\text{x}}{2}$

Answer

We are given,
$\text{y}=\frac{\text{x}}{2}$
Taking L.C.M ⇒ x - 2y = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 1; b = -2; c = 0

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Question 31 Mark

Write the following as an equation in two variables:
y = 3

Answer

We are given,
y = 3
Now, in two variable forms the given equation will be
0x + y - 3 = 0

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Question 41 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
4 = 3x

Answer

We are given,
4 = 3x
3x - 4 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 3; b = 0; c = -4

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Question 51 Mark

From the choices given below, choose the equation whose graph is given in Fig.

y = x
x + y = 0
y = 2x
2 + 3y = 7x

[Hint: Clearly, (-1, 1) and (1, -1) satisfy the equation x + y = 0]

Answer

Clearly (-1, 1) and (1, -1) satisfy the equation x + y = 0
$\therefore$ The equation whose graph is given is x + y = 0.

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Question 61 Mark

Write the following as an equation in two variables:
$5\text{x}=\frac{7}{ 2}$

Answer

We are given,
$5\text{x}=-\frac{7}{ 2}$
Now, in two variable forms the given equation will be
$5\text{x}+0\text{y}+\frac{7}{2} = 0$
$10\text{x}+0\text{y}-7=0$

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Question 71 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
$2\text{x} + 3\text{y} = 9.3\overline5$

Answer

We are given,
$2\text{x} + 3\text{y} = 9.3\overline5$
2x + 3y - 9.35 = 0
Comparing the given equation with ax + by + c = 0
We get, a = 2; b = 3; c = -9.35

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Question 81 Mark

Write the equation of the line that is parallel to y-axis and passing through the point:
(-4, -3)

Answer

The equation of the line that is parallel to y-axis and passing through (-4, -3) will be x = -4.

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Question 91 Mark

Write the equation of the line that is parallel to x-axis and passing through the point:
(0, 3)

Answer

The equation of the line that is parallel to x-axis and passing through the point (0, 3) is y = 3.

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Question 101 Mark

Write the equation representing y-axis.

Answer

The equation of line representing y-axis is given by x = 0

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Question 111 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
y - 5 = 0

Answer

We are given,
y - 5 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 0; b = 1; c = -5

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Question 121 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
2x + 3 = 0

Answer

We are given,
2x + 3 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 2; b = 0; c = 3

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Question 131 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
-2x + 3y = 12

Answer

We are given,
-2x + 3y = 12
-2x + 3y - 12 = 0
Comparing the given equation with ax + by + c = O
We get, a = -2; b = 3; c = -12

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Question 141 Mark

Write the following as an equation in two variables:
$\text{y}=\frac{3}{ 2}\text{x}$

Answer

We are given,
$\text{y}=\frac{3}{ 2}\text{x}$ (Taking L.C.M on both sides)
Now, in two variable forms the given equation will be
3x - 2y + 0 = 0

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Question 151 Mark

Write the equation of the line that is parallel to x-axis and passing through the point:
(3, 4)

Answer

The equation of the line that is parallel to x-axis and passing through the point (3, 4) is y = 4.

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Question 161 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
$\text{x}-\frac{\text{y}}{2}-5=0$

Answer

We are given,
$\text{x}-\frac{\text{y}}{2}-5=0$
Comparing the given equation with ax + by + c = 0,
We get, a = 1; $\text{b} =-\frac{1}{2},$ c = -5

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Question 171 Mark

A three-wheeler scooter charges ₹ 15 for first kilometer and ₹ 8 each for every subsequent kilometer. For a distance of x km, an amount of ₹ y is paid. Write the Linear equation representing the above information.

Answer

Total fare of ₹ y for covering distance of x kilometres is given by
y = 15 + 8(x - 1)
⇒ y = 15 + 8x - 8
⇒ y = 8x + 7
This is the required linear equation for the given information.

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Question 181 Mark

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid ₹ 27 for a book kept for seven days. If fixed charges are ₹ x and per day charges are ₹ y. Write the linear equation representing the abvoe information.

Answer

Total charges paid by Aarushi is given by
27 + x = 4y
⇒ x + 4y = 27
This is the required linear equation for the given information.

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Question 191 Mark

Write the equation of the line that is parallel to x-axis and passing through the point:
(2, -5)

Answer

The equation of the line that is parallel to x-axis and passing through the point (2, -5) is y = -5

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Question 201 Mark

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in case:
3x = -7y

Answer

We are given,
3x = -7y
3x + 7y = 0
Comparing the given equation with ax+ by + c = 0,
We get, a = 3; b = 7; c = 0

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Question 211 Mark

Write the equation of the line that is parallel to x-axis and passing through the point:
(0, -4)

Answer

The equation of the line that is parallel to x-axis and passing through the point (0, -4) is y = -4.

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Question 221 Mark

Write the following as an equation in two variables:
2x = -3

Answer

We are given,
2x = -3
Now, in two variable forms the given equation will be
2x + 0y + 3 = 0

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Question 231 Mark

Write the equation of the line that is parallel to y-axis and passing through the point:
(4, 0)

Answer

The equation of the line that is parallel to y-axis and passing through (4, 0) will be x = 4.

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Question 241 Mark

Write the equation of the line that is parallel to y-axis and passing through the point:
(-2, 0)

Answer

The equation of the line that is parallel to y-axis and passing through (-2, 0) will be x = -2.

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Question 251 Mark

Write the equation of the line that is parallel to y-axis and passing through the point:
(3, 5)

Answer

The equation of the line that is parallel to y-axis and passing through (3, 5) will be x = 3.

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Question 261 Mark

Give the equations of two lines passing through (3, 12) How many more such lines are there, and why?

Answer

We observe that x = 3 and y = 12 is the solution of the following equations
4x - y = 0 and 3x - y + 3 = 0
So, we get the equations of two lines passing through (3, 12) are, 4x - y = 0 and 3x - y + 3 = 0.
We know that passing through the given point infinitely many lines can be drawn. So, there are infinitely many lines passing through (3, 12)

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Question 271 Mark

Write the equation representing x-axis.

Answer

The equation of line representing x-axis is given by y = 0

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