Question

Decide whether the given point lies on the line. Justify your answer both algebraically and graphically. $$3 x-6 y=-2 ;(-4,-2)$$

Short answer

The point (-4, -2) does not lie on the line \(3x - 6y = -2\) both algebraically and graphically.

Step-by-step solution

Algebraic Justification

Substitute the x-coordinate and y-coordinate of the point into the equation of the line. The equation of the line is \(3x - 6y = -2\), and the point given is (-4, -2). After substituting, we get: \(3*-4 - 6*-2 = -2\), which simplifies to \(-12 + 12 = -2\). This simplifies further to \(0 = -2\). Since this is false, we can conclude that the point does not lie on the line.

Graphical Justification

Graph the line using the equation \(3x - 6y = -2\) by finding at least two points on the line and joining them with a straight line, then plot the point (-4, -2) on the graph. Since point (-4, -2) does not fall on the line that was sketched, we can conclude graphically that the point does not lie on the line.