graph the equation.\ny = 5|x|

Explanation:

Step1: Analyze when x≥0

When (x\geq0), (|x| = x), so the equation becomes (y = 5x). This is a linear - function with a slope of 5 and passes through the origin ((0,0)). We can find some points. For example, when (x = 1), (y=5\times1 = 5); when (x = 2), (y = 5\times2=10).

Step2: Analyze when x<0

When (x<0), (|x|=-x), so the equation becomes (y=-5x). This is also a linear - function. When (x=-1), (y=-5\times(-1) = 5); when (x=-2), (y=-5\times(-2)=10).

Step3: Plot the points

Plot the points ((0,0)), ((1,5)), ((2,10)), ((-1,5)), ((-2,10)) and connect them with straight - lines. The graph is a "V" shape with the vertex at the origin ((0,0)) opening upwards.

The graph of (y = 5|x|) is a V - shaped graph with the vertex at the origin ((0,0)) opening upwards. To graph it precisely, plot points for positive and negative (x) values based on the rules for the absolute - value function as described above.