Determine graphically, the vertices of the triangle formed by the lines
y = x, 3y = x and x + y = 8
Given linear equations are
y = x …(i)
3y = x …(ii)
and x + y = 8 …(iii)
For equation y = x,
If x = 1, then y = 1
If x = 0, then y = 0
If x = 2, then y = 2
Table for line y = x,
x | 0 | 1 | 2 |
y | 6 | 1 | 2 |
Points | O | A | B |
For equation x = 3y,
If x = 0, then y = 0. if x = 3, then y = 1, and if x = 6, then y = 2
Table for line x = 3y,
x | 0 | 3 | 6 |
Y | 0 | 1 | 2 |
Points | O | C | D |
For equation x + y = 8 or x = 8 - y
If x = 0, then y = 8, if x = 8, then y = 0 and if x = 4, then y = 4.
Table for line x + y = 8
x | 0 | 4 | 8 |
Y | 8 | 4 | 0 |
Points | P | Q | R |
Plotting the points A (1, 1) and B(2,2) we get the straight line AB.
Plotting the points C (3, 1) and D(6, 2), we get the straight line CD.
Plotting the point P (0, 8), Q(4, 4) and R(8, 0), we get the straight line PQR.
We see that lines AB and CD intersecting the line PR on Q and D, respectively.
So, 
is formed by these lines. Hence, the vertices of the 
formed by the given lines are O(0, 0), Q(4, 4) and D(6,2).