Mind Map

EQUATIONS OF LINES PARALLEL TO THE X-AXIS AND Y-AXIS: 

On the x-axis, the y-coordinate of each point is 0. In fact, every point on the x-axis is of the from (x, 0). Equation of the x-axis is given by y = 0

On the y-axis, the x-coordinate of each point is 0. In fact, every point on the y-axis is of the from (0, y). Equation of the y-axis is given by x = 0

y = 0 can be expressed as 0.x +1y = 0

x = 0 can be expressed as 1.x + 0.y = 0

question . What type of graph x + 4 = 0 and y – 4 = 0 will be?

Solution: x + 4 = 0 will be a graph parallel to y-axis.

y – 4 = 0 will be a graph parallel to x-axis.

Anys pair of values of x and y which satisfies the equation ax + by + c = 0, where a, b, c are non-zero real numbers, is called a solution of the equation. 

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

• If a ≠ 0, c ≠ 0 and b = 0. The equation ax + by + c = 0 reduces to ax + c = 0 or .x = -c/a
• The graph is a straight line. Parallel to y-axis and passing through the point (-c/a,0).
• If b ≠ 0, c ≠ 0 and a ≠ 0. The equation ax + by + c = 0 reduces to by + c = 0 or y = -c/b The graph is a straight line parallel to x-axis and passing through the point (0,-c/b)
• 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.

Geometric representation of ax + c = 0 as an equation 

• in one variable is x = -c/a
• in two variable is 

a.x + 0.y = −c.

•  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.