Question

If \(y+8=0,\) what is the slope of the graph? $$ \begin{array}{lllll} \text { (A) Undefined } & \text { (B) } 1 & \text { (C) } 0 & \text { (D) }-1 \end{array} $$

Short answer

The slope of the graph is 0. So, the correct answer is (C) 0.

Step-by-step solution

Identifying the form of the equation

The given equation is \(y + 8 = 0\). This equation can be rewritten as \(y = -8\) which matches the format of a linear equation \(y = mx + c\) where \(m\) is the slope and \(c\) is the y-intercept.

Recognizing the lack of x component

In the rewritten equation \(y = -8\), there is no \(x\) component. This means that for every \(x\), the \(y\) value does not change, it remains -8. This tells us that the line is horizontal.

Determining the slope

The slope of a line is a measure of the vertical change (the change in y-values) for each unit of horizontal change (the change in x-values). For a horizontal line, there is no vertical change regardless of the horizontal change, meaning the slope of a horizontal line is 0.