
How do you graph $ 4x = 2y + 6 $ using the $ x\;{\text{and}}\;y $ intercepts?
Answer
542.1k+ views
Hint: To graph the given equation using intercepts of the axes, first of all you have to find coordinates of both the intercepts and plot both the intercept point on a graph paper then join both the points and then extend the line in order to get the required graph.
Intercepts are calculated by putting the value of one variable zero in the equation to get an intercept of the other and vice versa.
Complete step-by-step answer:
In order to graph the given equation $ 4x = 2y + 6 $ using both intercepts, we will first find the $ x\;{\text{and}}\;y $ intercepts by putting value of one of them equals zero and get the other’s intercept and similarly do this process for the other one as follows
Finding $ x $ intercept by putting $ y = 0 $ in the given equation:
$
\Rightarrow 4x = 2 \times 0 + 6 \\
\Rightarrow 4x = 6 \\
\Rightarrow x = \dfrac{6}{4} = \dfrac{3}{2} \;
$
Therefore coordinate of $ x $ intercept can be written as \[\left( {\dfrac{3}{2},\;0} \right)\]
Similarly finding the $ y $ intercept, we will get
$
\Rightarrow 4 \times 0 = 2y + 6 \\
\Rightarrow 0 - 6 = 2y \\
\Rightarrow y = - \dfrac{6}{2} = - 3 \;
$
Therefore coordinate of $ y $ intercept can be written as \[\left( {0,\; - 3} \right)\]
Now, plotting these coordinates of intercepts on a graph paper, we will get
Now, joining the points and extending the line we get, then we will get
So, this is the required graph for the given equation.
Note: Intercepts method can only be applied or used when the given equation of straight line has intercepts or in other words, the equation which consists of constant term also with the variables have intercepts and so does this method is applicable.
Intercepts are calculated by putting the value of one variable zero in the equation to get an intercept of the other and vice versa.
Complete step-by-step answer:
In order to graph the given equation $ 4x = 2y + 6 $ using both intercepts, we will first find the $ x\;{\text{and}}\;y $ intercepts by putting value of one of them equals zero and get the other’s intercept and similarly do this process for the other one as follows
Finding $ x $ intercept by putting $ y = 0 $ in the given equation:
$
\Rightarrow 4x = 2 \times 0 + 6 \\
\Rightarrow 4x = 6 \\
\Rightarrow x = \dfrac{6}{4} = \dfrac{3}{2} \;
$
Therefore coordinate of $ x $ intercept can be written as \[\left( {\dfrac{3}{2},\;0} \right)\]
Similarly finding the $ y $ intercept, we will get
$
\Rightarrow 4 \times 0 = 2y + 6 \\
\Rightarrow 0 - 6 = 2y \\
\Rightarrow y = - \dfrac{6}{2} = - 3 \;
$
Therefore coordinate of $ y $ intercept can be written as \[\left( {0,\; - 3} \right)\]
Now, plotting these coordinates of intercepts on a graph paper, we will get
Now, joining the points and extending the line we get, then we will get
So, this is the required graph for the given equation.
Note: Intercepts method can only be applied or used when the given equation of straight line has intercepts or in other words, the equation which consists of constant term also with the variables have intercepts and so does this method is applicable.
Recently Updated Pages
Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

There are 720 permutations of the digits 1 2 3 4 5 class 11 maths CBSE

Discuss the various forms of bacteria class 11 biology CBSE

Draw a diagram of a plant cell and label at least eight class 11 biology CBSE

State the laws of reflection of light

Explain zero factorial class 11 maths CBSE

