Tag: using equations to plot lines

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Questions Related to using equations to plot lines

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

The nearest point on the line $3x-4y=25$ from the origin is

  1. $(-4,5)$
  2. $(3,-4)$
  3. $(3,4)$
  4. $(3,5)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance of the line $3x-4y-25=0$ from the origin is 
$\displaystyle d=\frac{|-25|}{\sqrt{25}}$
$\Rightarrow d=5$
Only the point given in option B lies on the given line .
Also, its distance from origin is 5.
So, (3,-4) is the nearest point on the line from the origin.

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

Consider the lines $2x+3y=0$,    $5x+4y=7$. Find the intersection point.

  1. $(3,-2)$
  2. $(3,2)$
  3. $(-3,2)$
  4. $(2,3)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The lines are $2x+3y=0$......(1)


$x=\dfrac{-3y}{2}$

$5x+4y=7$........(2)

$5\left(\dfrac{-3y}{2}\right)+4y=7$

$-15y+8y=14$

$-7y=14$

$y=-2$

$x=\dfrac{-3(-2)}{2}=3$

$(x,y)=(3,-2)$

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

$y=2x+3$
Which of the following statements is true about the given line?

  1. The line passes through $(0,3)$ and $m=-2$
  2. The line passes through $(3,0)$ and $m=-2$
  3. The line passes through $(0,3)$ and $m=2$
  4. The line passes through $(3,0)$ and $m=2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Comparing the given equation $y=2x+3$ with $y = mx+c$, we get

Hence, $m=2$ and $c=3$.
So, options A and B are incorrect.

Option C:
Substitute $(0,3)$ in the given equation, we get
RHS: $=2(0)+3 = 3$
LHS: $y=3$
$LHS =  RHS$, Hence option C is correct.

Option D:
Substitute $(3,0)$ in the given equation, we get
RHS: $=2(3)+3 = 9$
LHS: $y=0$

$LHS \neq RHS$. Hence, option D is incorrect.

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

Consider the equation of the line :$\displaystyle \frac{x-1}{3}-\frac{y+2}{2}=0$

  1. The line passes through $(4,0)$ and $m=2/3$
  2. The line passes through $(4,0)$ and $m=-2/3$
  3. The line passes through $(4,0)$ and $m=3/2$
  4. The line passes through $(4,0)$ and $m=-3/2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given line 
$\dfrac{x-1}{3}-\dfrac{y+2}{2}=0$

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

$2(x-1)=3(y+2)$

$2x-2=3y+6$

$y=\dfrac{2x}{3}-\dfrac{8}{3}$

on comparing above eq with $y=mx+c$

$slope(m)=\dfrac{2}{3}$

y-intercept$=-\dfrac{8}{3}$

when $y=0,x=4$

Hence it passes through $(4,0)$ with $m=\dfrac{2}{3}$
Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

Consider the line: y= -x +4

Which of the following is correct.

  1. The line passes through (0,4) and m=1.

  2. The line passes through (0,4) and m=-1.

  3. The line passes through (0,0) and m=-1.

  4. The line passes through (4,0) and m=-1.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given line 
$y=-x+4$
on comparing above eq with $y=mx+c$
$slope(m)=-1$
y-intercept$=4$
Hence it passes through (0,4) with $m=-1$
Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

Draw the graph for each linear equation:
$\displaystyle y=\frac{3}{2}x+\frac{2}{3}$

  1. The line passes through $(4/9,0)$ and $m=-\dfrac32$
  2. The line passes through $(-0.4/9,0)$ and $m=\dfrac32$
  3. The line passes through $(-4/9,0)$ and $m=\dfrac32$
  4. The line passes through $(-0.9/4,0)$ and $m=-\dfrac32$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The given line equation is $\frac{3}{2}x-y+\frac{2}{3}$

The slope of given line is $-(\frac { \frac { 3 }{ 2 }  }{ -1 } )=\frac { 3 }{ 2 } $
If we put $y=0$ , then the value of $x= -\frac{4}{9}$
Therefore line passes through $(-\frac{4}{9},0)$ and slope is $\frac{3}{2}$
So the correct option is $C$

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

Consider the equation of the line $\displaystyle x-3=\frac{2}{5}\left ( y-1 \right )$. Which of the following is correct?

  1. The line passes through $(6,5)$ and $m=-2/5$.
  2. The line passes through $(5,6)$ and $m=-5/2$.
  3. The line passes through $(6,5)$ and $m=2/5$.
  4. The line passes through $(5,6)$ and $m=5/2$.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given line 
$x-3=\dfrac{2}{5}(y-1)$
$5(x-3)=2(y-1)$
$5x-15=2y-2$
$2y=5x-13$
$y=\dfrac{5x}{2}-\dfrac{13}{2}$
on comparing above eq with $y=mx+c$
$slope(m)=\dfrac{5}{2}$

when $x=5$
$2y=25-13$
$2y=12$
$y=6$
Hence it passes through (5,6) with $m=\dfrac{5}{2}$
Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

For the pair of linear equations given below, draw graph and then state, whether the lines drawn are,
$\displaystyle y=3x-1$
$\displaystyle \frac{x}{2}+\frac{y}{3}=1$

  1. Perpendicular

  2. Parallel

  3. Intersecting but not at right angles

  4. Options B & C
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first line is y = 3x - 1 (slope m1 = 3). The second line x/2 + y/3 = 1 can be rewritten as y = -3/2x + 3 (slope m2 = -3/2). Since m1 is not equal to m2 and their product is not -1, the lines intersect but are not perpendicular.

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

For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are 
$\displaystyle 3x+4y=24$
$\displaystyle \frac{x}{4}+\frac{y}{3}=1$

  1. intersecting but not at right anglesl

  2. Options B & D

  3. perpendicular

  4. parallel
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The first line 3x + 4y = 24 has a slope of -3/4. The second line x/4 + y/3 = 1 can be rewritten as 3x + 4y = 12, which also has a slope of -3/4. Since the slopes are equal but the intercepts are different, the lines are parallel.