Mathematics
Does this help you to conclude anything about the linear equation y = ax + b when a is fixed but b varies?
Answer
Looking at the graphs of y = 2x – 1, y = 2x + 1 and y = 2x + 5, we observe:
The slope (a = 2) is the same for all three lines, so they are equally inclined and have the same direction.
The y-intercept (b) is different for each line:
For y = 2x – 1, the line cuts the y-axis at (0, -1).
For y = 2x + 1, the line cuts the y-axis at (0, 1).
For y = 2x + 5, the line cuts the y-axis at (0, 5).
The lines do not intersect each other; they are parallel to one another.
Hence, when a is fixed but b varies in the linear equation y = ax + b, the lines have the same slope but different y-intercepts, and they are parallel to each other.
Related Questions
Identify other points on the line y = 2x + 1 by completing the following table.
x y 1 3 2 5 7 15 9 12 20 
Differentiate between the graphs of the equations y = 3x + 1, and y = –3x + 1.
Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'.
(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 + 3Write a polynomial of degree 3 in the variable x, in which the coefficient of the x2 term is –7.