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
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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.
$x$
$y = 4x$
$y = 2x$
$y = x$
0
0
0
0
1
4
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 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
$a$
$b$
$y = 4x$
4
0
$y = 2x$
2
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 $a$ determines the slope: 4 > 2 > 1, so $y = 4x$ is the steepest and $y = x$ is the least steep.
