Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'.
(v) y = -2x - 3, y = -2x, y = -2x + 3
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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.
$x$
$y = -2x - 3$
$y = -2x$
$y = -2x + 3$
0
-3
0
3
1
-5
-2
1
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
$a$
$b$
$y = -2x - 3$
-2
-3
$y = -2x$
-2
0
$y = -2x + 3$
-2
3
4
Explain the roles of a and b in the three equations.
Answer: All three lines have $a = -2$, so they have the same slope and are parallel. Their $b$ values are -3, 0, and 3, which shift the lines vertically. Increasing $b$ moves the line upward, while decreasing $b$ moves it downward.
