Table of contents  
Linear Equations  
Equations of Lines parallel to the xaxis and yaxis 
1 Crore+ students have signed up on EduRev. Have you? 
An equation in two variables ‘x’ and ‘y’ in form of ax + by + c = 0 is called a linear equation. Such that a, b and c are real numbers.
Linear equation If we draw the graph of a degree one equation in two variables, we get a straight line.Every point on the graph of a linear equation is its solution. On the other hand, a solution of a linear equation always lies on the straight line representing the linear equation. Let us check that the point (2, 3) lies on the graph of 3x – 4y + 6 = 0.
We know that (2, 3) means x = 2 and y = 3,
L.H.S. = 3x – 4y + 6
= 3 x (2) – 4 x (3) + 6
= 6 – 12 + 6
= 12 – 12
= 0
= R.H.S.
Since L.H.S. = R.H.S. i.e. (2, 3) satisfy the equation 3x – 4y + 6 = 0.
A linear equation involves two variables x and y. By solution of a linear equation, we mean a pair of values, one for x and another for y which satisfy the given equation.
Note:
I. We write the solution of a linear equation as an ordered pair such that the first value for ‘x’ and then the value for ‘y’.
II. There is no end to different pairs of solution of a linear equation in two variables (i.e. a linear equation in two variables has infinitely many solutions).
We know that a ‘degree one’ polynomial in two variables has many solutions. These solutions are presented in the form of ordered pairs as (x, y). If we plot these ordered pairs on a graph paper and join them, we get a straight line.
Note: A ‘degree one’ polynomial equation ax + by + c = 0 is called a linear equation because its geometrical representation is a straight line.
To draw a graph of a linear equation of the form ax + by + c = 0, we take the followingsteps:
I. Express ‘y’ in terms of x.
II. Choose at least two or three values of x and find the corresponding values of y, satisfying the given equation.
III. Write these values of x and y in the form of a table.
IV. Plot the aboveordered pairs (x, y) on graph paper.
V. Joining these points, we get a straight line. This line is the required graph of the given equation.
Remember
I. Every point whose coordinates satisfy the given equation lies on the line.
II. Every point (l, m) on the line (the graph of the given equation) gives a solution x = l and y = m.
III. If a point does not lie on the graph line, it is not a solution of the equation.
I. Equation of the xaxis is y = 0.
II. Equation of the yaxis is x = 0.
III. Equation of a line parallel to the yaxis at a distance ‘m’ from it is x = 0 + m or x = m.
IV. Equation of a line parallel to the xaxis at a distance ‘n’ from it is y = 0 + n or y = n.
88 videos397 docs109 tests
