QUESTION 1
iii
Easy
Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'.
y = 5x, y = −5x
SOLUTION
1
Recall equation of a straight line
A straight line is written in the form \(y = ax + b\), where \(a\) is its slope and \(b\) is the \(y\)- intercept. Here, \(b = 0\).
2
Identify two points on each line
For \(y = 5x\):
When \(x = 1, y = 5\)
When \(x = −1, y = −5\)
So the two points are (\(1,5\)) and (\(−1,−5\))
For \(y = −5x\):
When \(x = 1, y = −5\)
When \(x = −1, y = 5\)
So the two points are (\(1,−5\)) and (\(−1,5\))
When \(x = 1, y = 5\)
When \(x = −1, y = −5\)
So the two points are (\(1,5\)) and (\(−1,−5\))
For \(y = −5x\):
When \(x = 1, y = −5\)
When \(x = −1, y = 5\)
So the two points are (\(1,−5\)) and (\(−1,5\))
3
Observe the role of '\(a\)' and '\(b\)'
In \(y = 5x\), \(a = 5\) and the line steeps upward.
In \(y = −5x\), \(a = −5\) and the line steeps downward.
The two lines are of the form \(y = ax\), so \(b = 0\), which means they all pass through the origin(\(0,0\)).
They form mirror image along \(x - \) axis.
In \(y = −5x\), \(a = −5\) and the line steeps downward.
The two lines are of the form \(y = ax\), so \(b = 0\), which means they all pass through the origin(\(0,0\)).
They form mirror image along \(x - \) axis.
Concept Note
Straight lines representing an equation of the form \(y = ax\) always pass through the origin(\(0,0\)).
When \(a > 1\), the line is steeper than the line \(y = x\), which is equally inclined to both axes. However, when \(a < 1\), the line is less steep than the line \(y = x\).