Answer:
Here we have two points R and S.
How many lines pass through both R and S?
Well, we can have only one line that passes through both R and S.
Because we are working with lines, we can only see a plane X-Y here.
Then the points R and S can be written as:
R = (x1, y1) and S = (x2, y2)
Now, a line or a linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now, let's suppose that we have two different lines that pass through points R and S.
From above, both lines must have the same slope, because they pass through the same points.
y1 = a*x + b
y2 = a*x + c
So the only thing that our lines can have different is the y-intercept, but the y-intercept acts as a vertical shift.
This means, if we have different values in the y-intercept, we will have two parallel lines.
And two parallel lines can never pass through the same points, which means that we can not have different values for the y-intercept.
Then the two lines must be identical.
Then there is only one line that passes through points S and R at the same time,
