Question

Express the given linear equation in the form \[ax+by+c=0\] and indicate the values of a, b and c in given case:
4 = 3x

Answer 1

- Hint: Express 4 = 3x as \[ax+by+c=0\], which is a linear equation. By comparing both the equations get the values of a, b and c.

Complete step-by-step answer: -
A linear equation between two variables that gives a straight line, they are the first degree equation as it has the highest exponent as variable as 1.
Here we are given, 4 = 3x.
We can write it as, 3x – 4 =0.
Here the equation has a homogeneous variable, i.e. the equation has only 1 variable, thus this type of equation is a linear equation in one variable.
Here y =0, i.e. a line equation is achieved by relating to zero.
Let us compare 3x – 4 = 0 with \[ax+by+c=0\].
We can write 3x – 4 = 0 as, 3x – 0y – 4 = 0 –(1)
Now comparing equation (1) with \[ax+by+c=0\], we can get the values of a, b and c as,
a = 3, b = 0, c = -4
Thus we have expressed the given equation in the form of \[ax+by+c=0\] and got values as a = 3, b = 0 and c = -4.

Note: If there was variable y, then it will be a linear equation with two variables.
e.g: 3x +2y – 4 =0, is a linear equation with two variables.
The solution of linear equations will generate values. In case of one variable there is only one solution for eg: - 3x = 4, \[x=\dfrac{4}{3}\] is the only solution.