Question

graph the image of e(-8, 3) after a reflection over the x-axis.

Explanation:

Step1: Recall the reflection rule over x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For the point \(E(-8,3)\), \(x=-8\) and \(y = 3\).

Step2: Apply the rule

Using the rule \((x,y)\to(x,-y)\), substitute \(x=-8\) and \(y = 3\).
We get the new \(y\) - coordinate as \(-3\) and the \(x\) - coordinate remains \(-8\). So the image of \(E(-8,3)\) after reflection over the \(x\) - axis is \(E'(-8,-3)\).

Answer:

The image of the point \(E(-8,3)\) after reflection over the \(x\) - axis is \(E'(-8,-3)\). On the graph, you would plot the point \((-8,-3)\) (8 units to the left of the \(y\) - axis and 3 units below the \(x\) - axis).