Question

The graph of the equation ay + b = 0 ( a & b are constants and a ≠ 0) will be x – axis,

when –

a) b =a
b) b = -a
c) b = 2
d) b = 0​

Answer 1

Answer:

An equation of the form ax + by + c = 0 where a, b, c are real numbers, a ≠ 0, b ≠ 0 and x, y are variables is called a linear equation in two variable.

Anys pair of values ofxandywhich satisfies the equation ax + by + c = 0, wherea, b, c are non-zero real numbers, is called a solution of the equation

• A linear equation in two variables has infinitely many solutions.

• Every point on the graph of a linear equation in two variables is a solution of the equation.

Geometric representation of ax + c = 0 as an equation

• in one variable is

• in two variable is

a.x + 0.y = –c.

• If a ≠ 0, c ≠ 0 and b = 0.

The equation

ax + by + c �� 0 reduces to ax + c = 0 or

The graph is a straight line. Parallel to y-axis and passing through the point

• If b ≠ 0, c ≠ 0 and a ≠ 0. The equation

ax + by + c = 0 reduces to by + c = 0 or The graph is a straight line parallel to x axis and passing through the point

• If a ≠ 0, b ≠ 0, c = 0 . The equation ax + by + c = 0 reduces to ax = 0 i.e. x= 0. The graph is y-axis itself

• If a = 0, b ≠ 0, c = 0. The equation ax + by + c = 0 reduces to by = 0 i.e. y= 0. The graph is x-axis itself

• If c = 0 , the equation ax + by + c = 0 reduces to ax + by = 0. The graph is a line passing through origin.