Answer
Verified
463.2k+ views
Hint: In this question, you need to understand that the given equation is of the form x=k, i.e., it represents a straight line parallel to y-axis when represented on a Cartesian plane. Also, looking at the equation, we can easily say that it passes through the point (5,0). So, you need to draw a line parallel to the y-axis and pass through the point (5,0) to represent the point on the graph.
Complete step-by-step answer:
Let us first find the general equations of the lines parallel to the y-axis.
We know the slope of the line parallel to the y-axis = slope of y-axis = $\infty =\dfrac{1}{0}$ .
Using general form of line, we get
$y=mx+c$
So, the equation of line becomes;
$y=\dfrac{1}{0}.x+c$
$\Rightarrow y-c=\dfrac{1}{0}.x$
On cross-multiplication, we get:
$0.(y-c)=x$
When c is finite;
The equation of the line parallel to y-axis come out to be;
$x=0$
When c is infinite:
We know, infinity multiplied by zero can give any value so let the value be ${{c}_{1}}$ .
We get, $x={{c}_{1}}$ .
As 0 is also a constant, the equation of line parallel to y-axis comes out to be: $x=k$
Where k is constant.
So, looking at the above equation, we can easily say that x=5 is the equation of the line i.e. parallel to y-axis. Also, looking at the equation we can easily say that the line will pass through the point (5,0). So, we will represent this line on the Cartesian plane, i.e., the graph.
Note: Avoid using intercept form of line for the lines parallel to x-axis and y-axis as you may get one of the intercepts to be infinity. Also, remember that the term graph generally refers to the Cartesian plane. However, if you are asked about the representation on the number line, then x=5 will be a point and on the 3-D plane x=5 will represent a plane.
Complete step-by-step answer:
Let us first find the general equations of the lines parallel to the y-axis.
We know the slope of the line parallel to the y-axis = slope of y-axis = $\infty =\dfrac{1}{0}$ .
Using general form of line, we get
$y=mx+c$
So, the equation of line becomes;
$y=\dfrac{1}{0}.x+c$
$\Rightarrow y-c=\dfrac{1}{0}.x$
On cross-multiplication, we get:
$0.(y-c)=x$
When c is finite;
The equation of the line parallel to y-axis come out to be;
$x=0$
When c is infinite:
We know, infinity multiplied by zero can give any value so let the value be ${{c}_{1}}$ .
We get, $x={{c}_{1}}$ .
As 0 is also a constant, the equation of line parallel to y-axis comes out to be: $x=k$
Where k is constant.
So, looking at the above equation, we can easily say that x=5 is the equation of the line i.e. parallel to y-axis. Also, looking at the equation we can easily say that the line will pass through the point (5,0). So, we will represent this line on the Cartesian plane, i.e., the graph.
Note: Avoid using intercept form of line for the lines parallel to x-axis and y-axis as you may get one of the intercepts to be infinity. Also, remember that the term graph generally refers to the Cartesian plane. However, if you are asked about the representation on the number line, then x=5 will be a point and on the 3-D plane x=5 will represent a plane.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which country is known as Cockpit of Europe aSwitzerland class 9 social science CBSE
What is a collective noun for bees class 10 english CBSE
Select the word which means the opposite of the given class 10 english CBSE
The supreme commander of the defense forces of India class 10 social science CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Which are the Top 10 Largest Countries of the World?
The highest rank in Indian Army is A General B Field class 9 social science CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which of the following is not a condition for becoming class 10 social science CBSE