Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'. Class 9

Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'. Class 9

Question 1.

Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'. Class 9

i. y = 4x, y = 2x, y = x

ii. y = -6x, y = -3x, y = -x

iii. y = 5x, y = -5x

iv. y = 3x - 1, y = 3x, y = 3x + 1

v. y = 2x - 3, y = -2x, y = 2x + 3.

Solution:

i. For y = 4x,

For y = 2x,

For y = x,

Since b = 0 for all three lines

∴ All lines pass through the origin and none of the lines shifts up or down.

As a increases from 1 to 4, the line becomes steeper.

Since a > 0 for all three lines

∴ All three lines represent linear growth.

ii. For y = -6x

For y = -3x

For y = -x

Since b = 0 for all three lines

∴ All lines pass through the origin and none of the lines shifts up or down.

As a increases from -6 to -1, the line becomes less steep

since a < 0 for all three lines

∴ All three lines represent linear decay.

iii. For y = 5x

For y = -5x

Since b = 0 for both lines y = -5x and y = 5x

∴ Both lines passes through origin

For y = -5x, a < 0

∴ y = -5x represents linear decay,

For y = 5x, a > 0

∴ y = 5x represents linear growth,

iv. For y = 3x - 1

For y = 3x

For y = 3x + 1

Since a = 3 for all the three lines

∴ The lines are parallel.

For y = 3x, b = 0

∴ It passes through the origin

For the lines y = 3x + 1 and y = 3x - 1, the y-intercepts are 1 and - 1 respectively.

i.e., the lines cut the y-axis at (1, 0) and (-1, 0) respectively.

v. For y = -2x - 3

For y = -2x

For y = 2x + 3

Since a = -2 for y = -2x - 3 and y = -2x,

∴ The two lines are parallel

Since a < 0, the two lines represent linear decay

Since a > 0 for y = 2x + 3, the line represents linear growth

Since b = 0 for y = 2x

∴ It passes through origin

For y = -2x - 3 and y = 2x + 3, the y-intercept are -3 and 3 respectively, i.e., the lines cuts y-axis at (0, -3) and (0, 3) respectively.