Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'.
(iii) y = 5x, y = -5x
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Answer
1
Choose a few values of x and find the corresponding y-values for both lines.
The table shows the corresponding $y$-values for each equation.
$x$
$y = 5x$
$y = -5x$
0
0
0
1
5
-5
2
Plot the points from the table and join the points for each equation to draw the two lines.
Answer: Both lines pass through (0, 0) and have equal steepness but opposite 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
$a$
$b$
$y = 5x$
5
0
$y = -5x$
-5
0
4
Explain the effect of changing the sign of a.
Answer: Both lines have $b = 0$ and $|a| = 5$, so they have equal steepness and pass through the origin. Changing the sign of $a$ changes the direction of the line: $y = 5x$ slopes upwards, while $y = -5x$ slopes downwards.
