Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'.
(iv) y = 3x - 1, y = 3x, y = 3x + 1
SponsoredDesktop Banner
Answer
1
Choose a few values of x and find the corresponding y-values for each line.
The table shows the corresponding $y$-values for each equation.
$x$
$y = 3x - 1$
$y = 3x$
$y = 3x + 1$
0
-1
0
1
1
2
3
4
2
Plot the points from the table and join the points for each equation to draw the three lines.
Answer: All three lines have the same slope and different y-intercepts.
3
Identify the slope a and y-intercept b of each line.
The table shows the slope $a$ and $y$-intercept $b$ of each line in the general form $y = ax + b$.
Line
$a$
$b$
$y = 3x - 1$
3
-1
$y = 3x$
3
0
$y = 3x + 1$
3
1
4
Explain the roles of a and b in the three equations.
Answer: All three lines have $a = 3$, so they have the same slope and are parallel. Their $b$ values are -1, 0, and 1, which shift the lines vertically. Increasing $b$ moves the line upward, while decreasing $b$ moves it downward.
