Question

Decide whether the given point lies on the line. Justify your answer both algebraically and graphically. $$x-y=10 ;(5,-5)$$

Short answer

Yes, the point (5,-5) lies on the line \( x - y = 10 \)

Step-by-step solution

Substitute the point into the line equation

The given line equation is \( x - y = 10 \). We can input the x value (5) and the y value (-5) from our point into the equation. This will give us \( 5 - (-5) = 10 \), which simplifies to \( 5 + 5 = 10 \), and thus \( 10 = 10 \).

Verification

As the left side of the equation equals the right side, the equation holds true. Therefore, it verifies that the given point (5,-5) lies on the line.

Graphical verification

To verify graphically, you should plot the line equation \( x - y = 10 \) and the point (5,-5) on a graph. If the point lies on the line, it confirms graphically that the point belongs to the line. As both algebraical and graphical confirmations align, we can be sure the point lies on the line.