graph the equation. y = 3|x|

Explanation:

Step1: Analyze when x≥0

When (x\geq0), (|x| = x), so the equation becomes (y = 3x). This is a straight - line with slope (m = 3) and y - intercept (b = 0). We can find some points on this line. For example, when (x = 0), (y=0); when (x = 1), (y = 3); when (x = 2), (y = 6).

Step2: Analyze when x<0

When (x<0), (|x|=-x), so the equation becomes (y=-3x). This is also a straight - line with slope (m = 3) and y - intercept (b = 0). For example, when (x=-1), (y = 3); when (x=-2), (y = 6).

Step3: Plot the points and draw the graph

Plot the points ((0,0)), ((1,3)), ((2,6)), ((-1,3)), ((-2,6)) and other points obtained from the above - mentioned rules on the coordinate plane. Then connect the points with straight lines. The graph is a "V" - shaped graph with the vertex at the origin ((0,0)) opening upwards.

Answer:

The graph is a "V" - shaped graph with vertex at ((0,0)) opening upwards, composed of the line (y = 3x) for (x\geq0) and (y=-3x) for (x<0).