Only one line can pass through a given point.
Step 1: Think of a single dot. Call it point \(P\).
Step 2: Draw one line through \(P\). This is possible.
Step 3: Now tilt your ruler a little and draw another line that still passes through \(P\). This new line is different from the first one.
Step 4: Keep changing the tilt (the “slope”). Every different tilt gives a new, different line through the same point \(P\).
Step 5 (tiny algebra idea): If the point is \(P(a,b)\), then all lines through \(P\) can be written as:
\(y - b = m(x - a)\)
Pick a slope value:
\(m = 0:\quad y = b\)
\(m = 1:\quad y - b = x - a\)
\(m = -2:\quad y - b = -2(x - a)\)
Conclusion: There are infinitely many choices of \(m\), so infinitely many different lines pass through a single point. The statement is false.