Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'.
(ii) y = -6x, y = -3x, y = -x
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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.
$x$
$y = -6x$
$y = -3x$
$y = -x$
0
0
0
0
1
-6
-3
-1
2
Plot the points from the table and join the points for each equation to draw the two lines.
Answer: All three lines pass through (0, 0) and have different slopes.
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
$a$
$b$
$y = -6x$
-6
0
$y = -3x$
-3
0
$y = -x$
-1
0
4
Explain the roles of a and b in the three equations.
Answer: All three lines have $b = 0$, so they pass through the origin. The coefficient $a$ is negative, so the lines slope downwards from left to right. The magnitude of $a$ determines the steepness: 6 > 3 > 1, so $y = -6x$ is the steepest.
