An algebraic equation having the highest degree of the variable as one is known as a linear equation. A linear equation can be in one variable say x
or it may have two variable say a, b. But in both the cases the highest degree of the variable in the linear equation is 1. A linear equation in two variables has its graph in the form of a straight line.
Which of the following equation is a linear equation? Support your answer by giving a suitable reason.
a. x + 2y = 5
– 3q + 7 = 0
For identifying a linear equation we need to recall the basic definition of linear equation. A linear equation is an equation with the variables having the highest degree as 1. So we check the highest degree of the variables in the given equations.
a. The highest degree is 1 for the variables x and y. So it is a linear equation.
b. The highest degree is 2 which is the power of p. Thus it is not a linear equation.
Write whether the given graph is of a linear equation? Give reasons for your answer.
a. As we already know that the graph of a linear equation is a straight line. In the given graph the curve is a straight line. This shows that the given graph is of a linear equation.
b. The given graph is a parabola and not a straight line. This proves that this graph is not a linear equation.