General form of linear equation
ax + by + c = 0
where, a, b and c are real numbers.
a and b are not equal to zero.
x, y = two variables.
- A linear equation in two variables has infinitely many solutions.
- The graph of every linear equation in two variables is a straight line.
- x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.
- The graph of x = a is a straight line parallel to the y-axis.
- The graph of y = a is a straight line parallel to the x-axis.
- An equation of the type y = mx represents a line passing through the origin
m = slope
Draw the lines of y = 2x and y =-2x
Solution of Linear Equation
a) Linear equation with a unique solution
b) Only two solutions
c) Infinitely many solutions
Total fare = y
total distance = x
y = 1 x 8 + (x – 1) 5
y = 8 + 5x – 5
y = 5x +3
5x -y +3 = 0
y = 5x +3
y(1) = 5 (1) + 3 = 8
y(7) = 5(2) + 3 = 13
y(3) = 5(3) + 3 = 18
Variable is classified into
- independent variable (x)
- dependent variable (y)
Draw the same graph in the third quadrant and find out at what point deg C = deg F
Draw the graph of the line joining the points (3, 5) and (-5, 1)
1. Draw the x-axis and y-axis on a graph
sheet with 1 cm = 1 unit on both axes.
2. We plot the two given points (3, 5),
(-5, 1) on the graph sheet.
3. We join the points by a line segment
and extend it on either direction.
4. We get the required linear graph.
Draw the graph of y = 6x
Linear equation – general form: ax + by + c = 0
y = 6x
y = dependent variable; also represented as y = f(x)
x = independent variable.
6x – y + 0 = 0
a = 6; b = -1; c = 0
Draw the graph of x = 5
Since x is constant, it is parallel to y axis. So, the point may be (5, y). Y becomes independent variable. We may give any value to y such as -2, 0, 2.
y = 4x -1
Draw the graph 2x + 3y = 12
A linear equation can also be represented as y = mx + c
where, m = slope
m = Δy/Δx
c = intercept
2x + 3y = 12
3y = -2x +12
y = 1/3 (-2x + 12)
y = -2x/3 + 12/3
y =(-2/3)x + 4
what is m?
m = -2/3
y intercept, c = (0, 4)
Problems for practice: