Problem 85 - Introductory Algebra for College Students

Question

Describe the graph of \(y=200\).

Step-by-Step Solution

Answer

The graph of \(y=200\) is a horizontal line intercepting the y-axis at the point (0,200). No matter what the x-value is, the y-value is always 200, resulting in a straight horizontal line.

Step 1: Identify the equation type

The equation \(y=200\) is a special type of linear equation, specifically a horizontal line. Linear equations are normally in the form \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept. In this case, there is no \(x\) term, so our slope \(m=0\), and the y-intercept \(b=200\).

Step 2: Draw the graph

Since the slope is 0, this line will be horizontal. And because the y-intercept is 200, that means this line crosses the y-axis at the point (0,200). So simply draw a horizontal line through the point (0,200) on the graph.

Step 3: Describe the graph

The graph of \(y=200\) is a horizontal line intercepting the y-axis at the point (0,200). It has a slope of 0, which means for any x-value, the y-value will always be 200.