What do all linear functions of the form f(x) = ax + a, a > 0, have in common? Class 9

What do all linear functions of the form f(x) = ax + a, a > 0, have in common? Class 9

Question 1.

What do all linear functions of the form f(x) = ax + a, a > 0, have in common? Class 9

Solution:

f(x) = ax + a, where a > 0

i. Slope:

The slope f(x) is a, and since a > 0,

∴ All the lines have positive slope.

ii. x-intercept:

To find where the lines cut the x-axis, put f(x) = 0

∴ ax + a = 0

∴ a(x + 1) = 0

∴ x + 1 = 0

∴ x = -1

iii. y-intercept:

To find where the line cuts the y-axis,

put x = 0 in f(x),

∴ f(0) = a(0) + a

∴ f(0) = a

Since a > 0,

∴ All the lines cut the y-axis above the origin.