Tag: reading graphs describing different situations

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Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

The straight lines given by the equations $\displaystyle x+y=2 , x-2y=5 \ and \ \frac{x}{3}+y=0$ are?

  1. concurrent

  2. intersecting to make a right triangle.

  3. intersecting to make an isosceles triangle.

  4. parallel to each other.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given lines
$x+y=2$------(1)
$x-2y=5$----(2) and $\dfrac{x}{3}+y=0$----(3)
Solving eq (1) and (2)
$x-2(2-x)=5$
$x-4+2x=5$
$x=3$ and $y=2-3=-1$
Point of intersection of line (1) and (2) is $P(3,-1)$
Solving eq (2) and (3)
$-3y-2y=5$
$-5y=5$
$y=-1$ and $x=-3y=3$
Point of intersection of line (2) and (3) is $Q(3,-1)$
Solving eq (1) and (3)
$-3y+y=2$
$-2y=2$
$y=-1$ and $x=-3y=3$
Point of intersection of line (1) and (3) is $R(3,-1)$
Here point of intersection of all line is same Hence line is concurrent
Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If the line ax + by + c = 0 is such that  a = 0 and b, $\displaystyle c\neq 0$ then the line is perpendicular to 

  1. x-axis

  2. y-axis

  3. x + y =1

  4. x = y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When $ a= 0 $ then the line equation becomes $ by + c = 0 $ or $ y = -\frac {c}{b} $

Equations of the form $ y =k $ are parallel to x-axis. This also means that they are perpendicular to $ y - $ axis as $ x-$ axis and $ y- $axis are perpendicular to each other.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

Find the equation of a line passing through the point (2, -3 ) and parallel to the line 2x - 3y + 8 = 0

  1. 2x - 3y =13

  2. 2x -3y = 12

  3. x - 3y =4

  4. 3x - 2y = 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Equation of the line parallel to $ 2x-3y+8 = 0 $ will be of the form $ 2x-3y + k = 0 $

Now, since it passes through $ (2,-3) $, on substituting it , we get $ 2(2) -3(-3) + k = 0  $
$ => k = -13 $

So, required eqn of parallel line is $ 2x - 3y - 13 = 0 $

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If $y$ is directly proportional to $x$ and if $y=20$  when $x=6$, what is the value of $y$ when $x=9$?

  1. $\displaystyle\frac{10}{3}$
  2. $\displaystyle\frac{40}{3}$
  3. $23$
  4. $27$
  5. $30$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Given that: $'y'$ is directly proportional to $'x'$,

Formally, it is expressed as
$y$ $=$ $k$$x$   where, $'k'$ is a constant
To find the value of $'k'$,
As $y$ $=$ $20$  when  $x$ $=$ $6$,
$\Rightarrow y$ $=$ $k$$x$
$\Rightarrow y$ $=$ $k$ $\times$ $x$
$\Rightarrow 20$ $=$ $k$ $\times$ $6$
$\Rightarrow k$ $=$ $\dfrac {20}{6}$
$\Rightarrow k$ $=$ $\dfrac {10}{3}$
Now, $y$ $=$ $\dfrac {10}{3}$$x$
To find $'y'$ when $x$ $=$ $9$,
$\Rightarrow y$ $=$ $\dfrac {10}{3}$$x$
$\Rightarrow y$ $=$ $\dfrac {10}{3}$ $\times$ $x$
$\Rightarrow y$ $=$ $\dfrac {10}{3}$ $\times$ $9$
$\Rightarrow y$ $=$ $30$

Therefore, the value of $'y'$ when $x$ $=$ $9$ is $'30'$.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If $y=2x+3$ and $x < 2$, which of the following represents all the possible values for $y$?

  1. $y < 7$
  2. $y > 7$
  3. $y < 5$
  4. $y > 5$
  5. $5 < y < 7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $y$ $=$ $2x$ $+$ $3$ and $x$ $<$ $2$

To find possible values for $y$,
$\Rightarrow 2x$ $=$ $y$ $-$ $3$
$\Rightarrow x$ $=$ $\dfrac {y \space - \space 3}{2}$
As $x$ $<$ $2$,
$\Rightarrow \dfrac {y \space - \space 3}{2}$  $<$ $2$
$\Rightarrow y$ $-$ $3$ $<$ $4$
$\Rightarrow y$ $<$ $7$
Therefore, possible values for $'y'$ are $'y$ $<$ $7'$.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

The graph of equation of the form $ax + by +c=0$ where a, b are non $-$ zero numbers,
represents:

  1. A triangle

  2. A ray

  3. A straight line

  4. a line segment
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation $ax+by+c=0$ represent straight line under one condition i. e, 

$|a|+|b|\neq 0$       or,     $ a\neq b\neq 0$
Also,  here
$y= \dfrac{-a}{b}x$ $  \dfrac{-c}{b}$ represent the slope interspect form where $m= (-a/b), y-m =  -c/b $ 

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

A right-angled triangle is formed by a straight line : $3x-4y=12$ with both the axis. Then length of perpendicular from the origin to the hypotenuse is :

  1. $3.5$
  2. $2.4$
  3. $4.2$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given straight line is $3x-4y=12$
$\Rightarrow\frac{x}{4}-\frac{y}{3} = 1$
this line have x intercept y & y- intercept (-3)
so the evaluation of hypotenuse s the given straight line $3x-4y=12$
so, distance of O(0, 0) form the line $3x-4y=12$ is given by
$=\frac{|3\times0-4\times0-12|}{\sqrt{(3)^2+(-4)^2}}$
$=\frac{12}{5}$
$=2.4$

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

The graph of the function $\displaystyle \cos x.\cos (x+2)-\cos^{2}(x+1)$ is a 

  1. straight line passing through the point $\displaystyle(0,-\sin^{2}1)$ with slope $2$

  2. straight line passing through the origin
  3. parabola with vertex $\displaystyle (1,-\sin^{2}1)$
  4. straight line passing through the point $\displaystyle\left(\dfrac{\pi}2,-\sin^{2}1\right) $ and parallel to the $x-$axis
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let $y=\cos { x } \cos { \left( x+2 \right)  } -\cos ^{ 2 }{ \left( x+1 \right)  } \ =\cos { \left( x+1-1 \right)  } \cos { \left( x+1+1 \right)  } -\cos ^{ 2 }{ \left( x+1 \right)  }\$
 Using $\cfrac{1}{2} \left[\cos\left(A+B+A-B\right)+\cos\left(A+B-A+B\right)\right]\
           = \cfrac{1}{2}\left[\cos 2A + \cos 2B\right]
           = \cfrac{1}{2}\left[\cos^{2}A -1 +1 -2 \sin^{2}A\right ]
           =  \cos ^{2}\left(x+1\right)-\sin^{2}1 $
$=\cos ^{ 2 }{ \left( x+1 \right)  } -\sin ^{ 2 }{ 1 } -\cos ^{ 2 }{ \left( x+1 \right)  } \ =-\sin ^{ 2 }{ 1 } $
This is a straight line which is parallel to x-axis, it passes through $\left( \cfrac { \pi  }{ 2 } ,-\sin ^{ 2 }{ 1 }  \right) $

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

Complete the table, to draw the graph of line $2y=3x+2$.


$x:$ $3$ $\displaystyle \frac{7}{3}$ $-2$
$y:$ $y _1$ $y _2$ $y _3$

  1. $y _1 = \dfrac12, y _2=\dfrac72,y _3 = -2$
  2. $y _1 = \dfrac{11}2, y _2=\dfrac92,y _3 = -2$
  3. $y _1 = \dfrac12, y _2=\dfrac72,y _3 = -3$
  4. $y _1 = \dfrac{11}2, y _2=\dfrac92,y _3 = -3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation of line is $2y=3x+2$

Now to complete the given table,
Substitute $x=3$ in the equation $2y=3x+2$ to fill the first column of the table
$\displaystyle 2y _1=3\times 3+2\ \Rightarrow 2y _1=9+2\ \Rightarrow 2y _!=11\ \Rightarrow y _!=\dfrac { 11 }{ 2 }$
 Substitute $x=\dfrac { 7 }{ 3 }$ in the equation $2y=3x+2$ to fill the second column of the table

$2y _2=3\times \dfrac { 7 }{ 3 } +2\\ \Rightarrow 2y _2=7+2\\ \Rightarrow 2y _2=9\\ \Rightarrow y _2=\dfrac { 9 }{ 2 }$
Finally, substitute $x=-2$ in the equation $2y=3x+2$ to fill the first column of the table
$2y _3=3\times -2+2\\ \Rightarrow 2y _3=-6+2\\ \Rightarrow 2y _3=-4\\ \Rightarrow y _3=-2$