Answer
Verified
422.7k+ views
Hint: To solve this we need to give the values of ‘x’ and we can find the values of ‘y’. Otherwise we can find the coordinate of the given equation lying on the line of x- axis, we can find this by substituting the value of ‘y’ is equal to zero (x-intercept). Similarly we can find the coordinate of the equation lying on the line of y- axis, we can find this by substituting the value of ‘x’ equal to zero (y-intercept).
Complete step-by-step answer:
Given, \[x - 4y = 12\] .
To find the x-intercept. That is the value of ‘x’ at \[y = 0\] . Substituting this in the given equation. We have,
\[x - 4(0) = 12\]
\[ \Rightarrow x = 12\]
Thus we have a coordinate of the equation which lies on the line of x-axis. The coordinate is \[(12,0)\] .
To find the y-intercept. That is the value of ‘y’ at \[x = 0\] . Substituting this in the given equation we have,
\[0 - 4y = 12\]
\[ - 4y = 12\] .
Divide by ‘-4’ on both sides of the equation,
\[y = - \dfrac{{12}}{4}\]
\[ \Rightarrow y = - 3\]
Thus we have a coordinate of the equation which lies on the line of y-axis. The coordinate is \[(0, - 3)\] .
Thus we have the coordinates \[(12,0)\] and \[(0, - 3)\] .
Let’s plot a graph for this coordinates,
We take scale
x-axis= 1 unit = 2 units
y-axis= 1 unit = 1 units
All we did was expand the line touching the coordinates \[(12,0)\] and \[(0, - 3)\] by a straight line.
Without calculation we have found out few more coordinates are \[(4, - 2)\] and \[(8, - 1)\].
Note: Intercept method is an easy method for drawing graphs. A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.
Complete step-by-step answer:
Given, \[x - 4y = 12\] .
To find the x-intercept. That is the value of ‘x’ at \[y = 0\] . Substituting this in the given equation. We have,
\[x - 4(0) = 12\]
\[ \Rightarrow x = 12\]
Thus we have a coordinate of the equation which lies on the line of x-axis. The coordinate is \[(12,0)\] .
To find the y-intercept. That is the value of ‘y’ at \[x = 0\] . Substituting this in the given equation we have,
\[0 - 4y = 12\]
\[ - 4y = 12\] .
Divide by ‘-4’ on both sides of the equation,
\[y = - \dfrac{{12}}{4}\]
\[ \Rightarrow y = - 3\]
Thus we have a coordinate of the equation which lies on the line of y-axis. The coordinate is \[(0, - 3)\] .
Thus we have the coordinates \[(12,0)\] and \[(0, - 3)\] .
Let’s plot a graph for this coordinates,
We take scale
x-axis= 1 unit = 2 units
y-axis= 1 unit = 1 units
All we did was expand the line touching the coordinates \[(12,0)\] and \[(0, - 3)\] by a straight line.
Without calculation we have found out few more coordinates are \[(4, - 2)\] and \[(8, - 1)\].
Note: Intercept method is an easy method for drawing graphs. A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.
Recently Updated Pages
Fill in the blanks with a suitable option She showed class 10 english CBSE
TISCO is located on the banks of which river A Tungabhadra class 10 social science CBSE
What is greed for clothes A Simply desire to have them class 10 social science CBSE
What does the 17th Parallel line separate A South and class 10 social science CBSE
The original home of the gypsies was A Egypt B Russia class 10 social science CBSE
The angle between the true north south line and the class 10 social science CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Which are the Top 10 Largest Countries of the World?
Which is the longest day and shortest night in the class 11 sst CBSE
What is the definite integral of zero a constant b class 12 maths CBSE
Name five important trees found in the tropical evergreen class 10 social studies CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE