Question

Draw the graph of 3x+2=5x-4 A) in one variable B) in two variable

Answer 1

Step-by-step explanation:

Draw the graph of each of the following linear equations in two variables:

(i) x + y = 4 ii) x – y = 2 (iii) y = 3x (iv) 3 = 2x + y

Sol: (i) x + y = 4 ⇒ y = 4 – x

If we have x = 0, then y = 4 – 0 = 4

x = 1, then y = 4 – 1 = 3

x = 2, then y = 4 – 2 = 2

∴ We get the following table:

Plot the ordered pairs (0, 4), (1, 3) and (2, 2) on the graph paper. Joining these points, we get a line AB as shown below.

Thus, the line AB is the required graph of x + y = 4.

(ii) x – y = 2

⇒ y = x – 2

If we have x = 0,then y = 0 – 2 = –2

x = 1,then y = 1 – 2 = –1

x = 2, then y = 2 – 2 = 0

∴ We have the following table:

Plot the ordered pairs (0, –2), (1, –1) and (2, 0) on the graph paper. Joining these points, we get a straight line PQ as shown below:

Thus, the line PQ is required graph of x – y = 2.

(iii) y = 3x

If x = 0, then y = 3(0) ⇒ y = 0

x = 1, then y = 3(1) ⇒ y = 3

x = –1, then y = 3(–1) ⇒ y = –3

∴ We get the following table:

Plot the ordered pairs (0, 0), (1, 3) and (–1, –3) on the graph paper. Joining these points, we get the straight line LM.

Thus, LM is the required graph of y = 3x.

Note: The graph of the equation of the form y – kx is a straight line which always passes through the origin.

(iv) 3 = 2x + y ⇒ y – 3 – 2x

∴ If x = 0, then y = 3 – 2(0) ⇒ y = 3

If x = 1, then y = 3 – 2(1) ⇒ y = 1

If x = 2, then y = 3 – 2(2) ⇒ y = –1

Plot the ordered pairs (0, 3), (1, 1) and (2, 1) on the graph paper. Joining these points, we get a line CD.

Thus, the line CD is the required graph of 3 –2x–ry