4 Marks Questions

Question 14 Marks

Write the linear equation such that each point on its graph has an ordinate $3$ times its abscissa.

Answer

Let the abscissa of the point be $x,$ According to the question, Ordinate $(y) = 3$ $x$ Abscissa $⇒ y= 3x$ When $x = 1,$ then $y = 3 × 1 = 3$ and when $x = 2,$ then $y = 3 × 2 = 6.$

$x$	$1$	$2$
$y$	$3$	$6$

Here, we find two points $A(1, 3)$ and $B(2, 6)$. So, draw the graph by plotting the points and joining the line $AB.$

Hence, $y = 3x$ is the required equation such that each point on its graph has an ordinate 3 times its abscissa.

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Question 24 Marks

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to $6 \ kg$. Read from the graph, the force required when the acceleration produced is:
$i. 5\ ms^{-2}$
$ii.\ ms^{-2}$

Answer

Given that, the force $(F)$ is directly proportional to the the acceleration $(a)$
i.e. $\text{F}\propto\text{a}$
$\Rightarrow\text{F}=\text{ma} [$where $m =$ arbitary constant and take value $6\ kg$ of mass$]$ $\therefore\text{F}=6\text{a}$
$i.$ If $\text{a}=5\frac{\text{m}}{\text{s}}^2$ then from $Eq (i),$ we get
$F = 6 \times 5 = 30N$
$ii.$ If $\text{a}=6\frac{\text{m}}{\text{s}}^2$ then from $Eq (i),$ we get
$F = 6 \times 6 = 36N$
Here, we find two points $A(5, 30)$ and $B(6, 36).$
So draw the graph by plotting the point and joining the line $AB.$

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Question 34 Marks

Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as $10$ units.

Answer

As per question, the sum of the coordinates is $10$ units. Let $x$ and $y$ be two coordinates, then we get $x + y = 10.$

For $x = 5, y = 5,$ therefore, $(5, 5)$ lies on the graph of $x + y = 10.$
For $x = 3, y = 7,$ therefore, $(3, 7)$ lies on the graph of $x + y = 10.$
Now, plotting the points $(5, 5)$ and $(3, 7)$ on the graph paper and joining them by a line,
we get graph of the linear equation $x + y = 10.$

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Maths 4 Marks Questions

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