Question 11 Mark
Write the equation of the line that is parallel to $y$-axis and passing through the point: $(3, 5)$
AnswerThe equation of the line that is parallel to $y-$axis and passing through $(3, 5)$ will be $x = 3.$
View full question & answer→Question 21 Mark
Write the equation of the line that is parallel to $x-$axis and passing through the point: $(0, 3)$
AnswerThe equation of the line that is parallel to $x-$axis and passing through the point $(0, 3) $is $y = 3.$
View full question & answer→Question 31 Mark
Write the following as an equation in two variables: $5\text{x}=\frac{7}{ 2}$
AnswerWe are given, $5\text{x}=-\frac{7}{ 2}$ Now, in two variable forms the given equation will be $5\text{x}+0\text{y}+\frac{7}{2} = 0$ $10\text{x}+0\text{y}-7=0$
View full question & answer→Question 41 Mark
Write the equation of the line that is parallel to $x-$axis and passing through the point: $(2, -5)$
AnswerThe equation of the line that is parallel to $x-$axis and passing through the point $(2, -5)$ is $y = -5$
View full question & answer→Question 51 Mark
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in case: $3x = -7y$
AnswerWe are given, $3x = -7y 3x + 7y = 0$ Comparing the given equation with $ax+ by + c = 0,$ We get, $a = 3; b = 7; c = 0$
View full question & answer→Question 61 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.
AnswerTotal charges paid by Aarushi is given by $27+x=4 y \Rightarrow x+4 y=27$ This is the required linear equation for the given information.
View full question & answer→Question 71 Mark
Give the equations of two lines passing through $(3, 12)$ How many more such lines are there, and why?
AnswerWe 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 $(3, 12)$
View full question & answer→Question 81 Mark
From the choices given below, choose the equation whose graph is given in Fig.
$i.y = x + 2$
$ii.y = x - 2$
$iii.y = -x + 2$
$iv.x = 2y = 6$
$[$Hint: Clearly $(2, 0)$ and $(-1, 3)$ satisfy the equation $y = -x + 2]$ AnswerClearly $(2, 0)$ and $(-1, 3)$ satisfy the equation $y = -x + 2.$
$\therefore$ The equation whose graph is given is $y = -x + 2.$
View full question & answer→Question 91 Mark
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in case: $\text{y}=\frac{\text{x}}{2}$
AnswerWe are given, $\text{y}=\frac{\text{x}}{2}$ Taking $L.C.M \Rightarrow x - 2y = 0$ Comparing the given equation with $ax + by + c = 0$, We get, $a = 1; b = -2; c = 0$
View full question & answer→Question 101 Mark
Write the following as an equation in two variables: $y = 3$
AnswerWe are given, $y = 3$ Now, in two variable forms the given equation will be $0x + y - 3 = 0$
View full question & answer→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: $4 = 3x$
AnswerWe are given, $4 = 3x 3x - 4 = 0$ Comparing the given equation with $ax + by + c = 0$, We get, $a = 3; b = 0; c = -4$
View full question & answer→Question 121 Mark
From the choices given below, choose the equation whose graph is given in Fig.
$1. y = x$
$2. x + y = 0$
$3. y = 2x$
$4. 2 + 3y = 7x$
$[$Hint: Clearly, $(-1, 1)$ and $(1, -1)$ satisfy the equation $x + y = 0]$ AnswerClearly $(-1, 1)$ and $(1, -1)$ satisfy the equation $x + y = 0$
$ \therefore$ The equation whose graph is given is $x + y = 0.$
View full question & answer→Question 131 Mark
Express the following linear equations in the form $a x+b y+c=0$ and indicate the values of $a, b$ and $c$ in case: $-2 x+3 y= 12$
AnswerWe are given, $-2 x+3 y=12-2 x+3 y-12=0$ Comparing the given equation with $a x+b y+c=0$ We get, $a=-2 ; b=3 ; c$ $=-12$
View full question & answer→Question 141 Mark
Write the equation representing $x-$axis.
AnswerThe equation of line representing x-axis is given by $y = 0$
View full question & answer→Question 151 Mark
Write the equation of the line that is parallel to $x-$axis and passing through the point:
$(0, -4)$
AnswerThe equation of the line that is parallel to $x-$axis and passing through the point $(0, -4)$ is $y = -4.$
View full question & answer→Question 161 Mark
Write the equation of the line that is parallel to x-axis and passing through the point: $(3, 4)$
AnswerThe equation of the line that is parallel to $x-$axis and passing through the point $(3, 4)$ is $y = 4.$
View full question & answer→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.
AnswerTotal fare of ₹ $y$ for covering distance of $x$ kilometres is given by
$y = 15 + 8(x - 1)$
$\Rightarrow y = 15 + 8x - 8$
$\Rightarrow y = 8x + 7$
This is the required linear equation for the given information.
View full question & answer→Question 181 Mark
Write the following as an equation in two variables: $2x = -3$
AnswerWe are given, $2x = -3$ Now, in two variable forms the given equation will be$ 2x + 0y + 3 = 0$
View full question & answer→Question 191 Mark
Write the equation of the line that is parallel to y-axis and passing through the point: $(4, 0)$
AnswerThe equation of the line that is parallel to $y-$axis and passing through $(4, 0)$ will be $x = 4.$
View full question & answer→Question 201 Mark
Write the equation representing $y-$axis.
AnswerThe equation of line representing $y-$axis is given by $x = 0$
View full question & answer→Question 211 Mark
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in case: $2\text{x} + 3\text{y} = 9.3\overline5$
AnswerWe 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, $a = 2; b = 3; c = -9.35$
View full question & answer→Question 221 Mark
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in case: $\text{x}-\frac{\text{y}}{2}-5=0$
AnswerWe are given, $\text{x}-\frac{\text{y}}{2}-5=0$ Comparing the given equation with $ax + by + c = 0$, We get, $a = 1; \text{b} =-\frac{1}{2}, c = -5$
View full question & answer→Question 231 Mark
Write the following as an equation in two variables: $\text{y}=\frac{3}{ 2}\text{x}$
AnswerWe 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 $3x - 2y + 0 = 0$
View full question & answer→Question 241 Mark
Write the equation of the line that is parallel to $y-$axis and passing through the point: $(-4, -3)$
AnswerThe equation of the line that is parallel to $y-$axis and passing through $(-4, -3)$ will be $x = -4.$
View full question & answer→Question 251 Mark
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in case: $y - 5 = 0$
AnswerWe are given, $y - 5 = 0$ Comparing the given equation with $ax + by + c = 0$, We get, $a = 0; b = 1; c = -5$
View full question & answer→Question 261 Mark
Express the following linear equations in the form $a x+b y+c=0$ and indicate the values of $a, b$ and $c$ in case: $2 x+3=0$
AnswerWe are given, $2 x+3=0$ Comparing the given equation with $a x+b y+c=0$, We get, $a=2 ; b=0 ; c=3$
View full question & answer→Question 271 Mark
Write the equation of the line that is parallel to $y-$axis and passing through the point: $(-2, 0)$
AnswerThe equation of the line that is parallel to $y-$axis and passing through $(-2, 0)$ will be $x = -2.$
View full question & answer→Question 281 Mark
Find the value of k for which x = underline 1, y = - 2 is a solution of the linear equation x - 2y + k = 0
Question 291 Mark
If x = a y = 2 is a solution of the linear equation 2x - 3y + 8 = 0 find the value of a.
Question 301 Mark
Solve the equation 2y - 1 = y + 1 and represent it graphically on the coordinate plane
Question 311 Mark
Solve the equation 3x - 2 = 2x + 3 and represent the solution on the number line.
Question 321 Mark
A line passes through the point (-4, 6) and is parallel to x-axis. Find its equation.
Question 331 Mark
Write the equation of a line parallel to y-axis and passing through the point (-3, -7).
Question 341 Mark
Write the equation of a line passing through the point (3, 5) and parallel to x-axis.
Question 351 Mark
Write the equation of a line passing through the point (0, 4) and parallel to x-axis.
Question 361 Mark
Write the equation representing y-axis.
Question 371 Mark
Write the equation representing x-axis