Question

Draw the graph of the linear equation 2x - y + 1 = 0. From your graph, find the values of h and k if graph passes through the points (h,4) and (1/2,k)

Answer 1

Linear equations have infinitely many solutions.

2. Every point (h, k) on the line AB gives the solution x = h and y = k.

3. Every point which lies on AB satisfies the equation of AB.

4. To draw an exact line on the graph paper you can plot as many points you like, but it is necessary to plot minimum three points.

Method to draw the graph of linear equation in two variables:

1. Convert the given equation in the form of y = mx + b (slope intercept form).

2. Apply trial and error method to find 3 pairs of values of (x, y) which satisfy the given equation.

3. Plot these points on the graph paper.

4. Join the points marked on the graph paper to get a straight line which represent the given equation graphically.


Note:

1. Linear equation in two variables has infinitely many solutions.

2. A graph of linear equation is always a straight line.

3. Every point on the straight line is the solution of the linear equation.

4. Equation of y-axis is x = 0. The standard form of this equation is x + 0.y = 0.

5. Equation of x-axis is y = 0. The standard form of this equation is 0.x + y = 0.

6. x = a is a graph of straight line parallel to y-axis and standard form of this equation is x + 0.y = a

7. y = b is a graph of straight line parallel to x-axis and standard form of this equation is 0.x + y = b.

8. The equation y = mx is always passing through the origin (0, 0).


Learn the steps for graphing linear equation in two variables:

1. Draw the graph of the linear equation y = 2x.

Solution:            

The given linear equation y = 2x is already in the form of y = mx + b [here b = 0]. 

Now we will apply the trial and error method to find 3 pairs of values of (x, y) which satisfy the given equation y = 2x.

When the value of x = 0, then y = 2 × 0 = 0

When the value of x = 1, then y = 2 × 1 = 2

When the value of x = 3, then y = 2 × 3 = 6

When the value of x = -1, then y = 2 × -1 = -2

When the value of x = -2, then y = 2 × -2 = -4

Arrange the values of the linear equation y = 2x in the table.