graph this function: y = 5|x| click to plot the vertex first.

Explanation:

Step1: Identify the vertex

For the absolute - value function $y = a|x - h|+k$, the vertex is $(h,k)$. In the function $y = 5|x|$, $h = 0$ and $k = 0$, so the vertex is $(0,0)$. Plot the point $(0,0)$ on the graph.

Step2: Find points for $x>0$

When $x>0$, the function is $y = 5x$. Let's choose $x = 1$, then $y=5\times1 = 5$. So we have the point $(1,5)$. Let $x = 2$, then $y = 5\times2=10$, giving the point $(2,10)$.

Step3: Use symmetry

Since $y = 5|x|$ is an even function (symmetric about the y - axis), for the point $(x,y)$ on the right - hand side of the y - axis, the point $(-x,y)$ is on the left - hand side. So the points $(-1,5)$ and $(-2,10)$ are also on the graph. Plot these points and draw a V - shaped graph passing through them.

Answer:

Plot the vertex at $(0,0)$, then plot points $(1,5),(2,10),(-1,5),(-2,10)$ and draw a V - shaped graph.