QUESTION 1
ii
Easy
Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'.
y = −6x, y = −3x, y = −x
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 \(y = −6x\):
When \(x = 1, y = −6\)
When \(x = −1, y = 6\)
So the two points are (\(1,−6\)) and (\(−1,6\))
For \(y = −3x\):
When \(x = 1, y = −3\)
When \(x = −1, y = 3\)
So the two points are (\(1,−3\)) and (\(−1,3\))
For \(y = −x\):
When \(x = 1, y = −1\)
When \(x = −1, y = 1\)
So the two points are (\(1,−1\)) and (\(−1,1\))
When \(x = 1, y = −6\)
When \(x = −1, y = 6\)
So the two points are (\(1,−6\)) and (\(−1,6\))
For \(y = −3x\):
When \(x = 1, y = −3\)
When \(x = −1, y = 3\)
So the two points are (\(1,−3\)) and (\(−1,3\))
For \(y = −x\):
When \(x = 1, y = −1\)
When \(x = −1, y = 1\)
So the two points are (\(1,−1\)) and (\(−1,1\))
3
Observe the role of '\(a\)' and '\(b\)'
As slope(\(a\)) increases, the line gets steeper.
The three lines are of the form \(y = ax\), so \(b = 0\), which means they all pass through the origin(\(0,0\)).
The three lines are of the form \(y = ax\), so \(b = 0\), which means they all pass through the origin(\(0,0\)).
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 \(y = x\).