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Chapter 0: Problem 18

Graph. List the slope and \(y\) -intercept. $$y=-5$$

Short Answer

Expert verified
Slope: 0, y-intercept: -5.

Step by step solution

01

Identify the Equation Form

The given equation is in the form of y = cwhere c is a constant.
02

Analyze the Slope

In the equation y = -5the value of y is constant and does not depend on x. This means that the slope (m) of the line is zero, as there is no x-term.
03

Determine the y-intercept

The y-intercept is the value of y when x is 0. From the equation y = -5,it is clear that the y-intercept is -5. This means the line intersects the y-axis at the point (0, -5).
04

Summarize the findings

To summarize, the line y = -5 has a slope of 0 and a y-intercept of -5. This is a horizontal line passing through y = -5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

slope
Understanding the slope of a line is crucial for graphing linear equations. The slope, often denoted as \(m\), indicates how steep the line is. It tells us how much the y-value changes for a unit change in the x-value.
In the equation \(y = -5\), there is no x-term present. This means the y-value does not change, no matter what x is. Since the change in y is zero, the slope of the line is \(0\).
A zero slope represents a perfectly horizontal line.
A quick way to remember this:
  • Positive slope: line rises (uphill)
  • Negative slope: line falls (downhill)
  • Zero slope: horizontal line
  • Undefined slope: vertical line
y-intercept
The y-intercept is where the line crosses the y-axis. This point shows the value of y when x is \(0\). In the given equation \( y = -5 \), it is clear that the line intersects the y-axis at -5.
To find the y-intercept in other equations, set \(x\) to zero and solve for \(y\):
  • In \(y = mx + b\), the y-intercept is \(b\).
  • With \(y = -5\), since there is no x-term, we see directly that the y-intercept is -5.
To graph it, simply start at \( (0, -5) \) on the y-axis.
horizontal lines
Horizontal lines are unique in that they have no slope 鈥� their slope is \(0\). These lines run left to right across the graph and are perfectly flat.
For example, the line \(y = -5\) is a horizontal line. This means:
  • It passes through the y-axis at \(y = -5\)
  • Every point on the line has a y-coordinate of -5, regardless of the x-coordinate
To graph this, draw a straight line across the graph at \(y = -5\).
Understanding horizontal lines is important:
  • They have zero slope (flat)
  • They intersect the y-axis at a single point

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