Answer
Verified
409.2k+ views
Hint: We are given y varies directly with x, to find the equation for this we will first see what type of relations we have and we will learn about inverse and direct relation and using these we will find the relation suitable for our problem. We will use that directly as the relation is given as y = kx where k is a constant. Then we will use x = 5, y = 25 to find the value of k.
Complete step-by-step solution:
We are given that y varies directly with x, we are asked to write the direct linear variation equation. Before we move on to that we must learn what direct relation means. In maths, there are two types of relation, one is called direct relation and the other is indirect relation (inversely). In direct relation, two things are connecting directly means they both will behave the same way if there is a decrement in one thing then the other will decrease too and if one is increasing then other will increase too, say we have two things as A and B. They are denoted as \[A\propto B.\] The sign \['\propto '\] is called a sign of proportionality. To form an equation we need to change the proportional \[\left( \propto \right)\] to equal (=). So, we will multiply by constant. So, the equation becomes A = kB. The other type of relation is indirectly where A is moving opposite of B. If A increases, B will decrease and if A decreases B will increase. It is represented as \[A\propto \dfrac{1}{B}.\]
Now, in our problem, we have that we have two things as y and x. We also have that y is directly proportional to x. So, as we learn above, we will get, \[y\propto x.\] To change \[\propto \] to =, we will multiply by constant, say k, we will get \[y=kx.\] So, the required equation is y = kx. Now, as we have for x = 5, we have y = 25, so putting them in our equation, we get,
\[25=k\left( 5 \right)\]
Dividing both the sides by 5, we get,
\[\Rightarrow 5=k\]
So, the value of the constant k is 5.
Hence the equation is y = 5x.
Note: The graph of the direct relation will always produce a straight line. If the constant of proportionality is positive, then the graph will have a positive gradient. If the constant is negative, then the graph will have a negative gradient.
Complete step-by-step solution:
We are given that y varies directly with x, we are asked to write the direct linear variation equation. Before we move on to that we must learn what direct relation means. In maths, there are two types of relation, one is called direct relation and the other is indirect relation (inversely). In direct relation, two things are connecting directly means they both will behave the same way if there is a decrement in one thing then the other will decrease too and if one is increasing then other will increase too, say we have two things as A and B. They are denoted as \[A\propto B.\] The sign \['\propto '\] is called a sign of proportionality. To form an equation we need to change the proportional \[\left( \propto \right)\] to equal (=). So, we will multiply by constant. So, the equation becomes A = kB. The other type of relation is indirectly where A is moving opposite of B. If A increases, B will decrease and if A decreases B will increase. It is represented as \[A\propto \dfrac{1}{B}.\]
Now, in our problem, we have that we have two things as y and x. We also have that y is directly proportional to x. So, as we learn above, we will get, \[y\propto x.\] To change \[\propto \] to =, we will multiply by constant, say k, we will get \[y=kx.\] So, the required equation is y = kx. Now, as we have for x = 5, we have y = 25, so putting them in our equation, we get,
\[25=k\left( 5 \right)\]
Dividing both the sides by 5, we get,
\[\Rightarrow 5=k\]
So, the value of the constant k is 5.
Hence the equation is y = 5x.
Note: The graph of the direct relation will always produce a straight line. If the constant of proportionality is positive, then the graph will have a positive gradient. If the constant is negative, then the graph will have a negative gradient.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE