Answer
Check Explanation.
Explanation
The equation of the straight line is given, we are then told to obtain 3 points and plot it on the graph.
The equation of the straight line given is
x - 3y = 6
The equation of straight lines are usually best represented in the form
y = mx + c
So, we will put the given equation in that format.
x - 3y = 6
-3y = -x + 6
Multiply both sides by -1
3y = x - 6
Divide through by 3
(3y/3) = (x/3) - (6/3)
y = (x/3) - 2
y = 0.3333x - 2
So, we now find 3 points on the line in order to plot it on your graph.
In picking points while plotting graphs, it is easier to
- first pick the point where x = 0, calculate y
- Then pick the point where y = 0, calculate x,
- We can then pick one more arbitrary point and calculate the corresponding other coordinates there.
So, when x = 0,
y = 0.3333x - 2
y = (0.3333 × 0) - 3 = 0 - 2 = -2
when x = 0, y = -2.
First point is (0, -2)
when y = 0,
y = 0.3333x - 2
0 = 0.3333x - 2
0.3333x = 2
x = (2/0.3333) = 6
when y = 0, x = 6.
Second point is (6, 0)
Then for the third point, we arbitrarily pick when x = 3,
y = 0.3333x - 2
y = (0.3333 × 3) - 2 = 1 - 2 = -1
when x = 3, y = -1
Third point is (3, -1)
Hence, the three points that will help us plot the graph of the straight line are
(0, -2), (6, 0) and (3, -1)
Now, I'll need you to mark these points on the graph provided and join the points together to form a straight line as shown in the image I will attach now.
So, this is the graph of x - 3y = 6.
Hope this Helps!!!