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Chapter 3: Problem 47

Graph each linear equation. \(y=-1\)

Short Answer

Expert verified
Horizontal line at y=-1.

Step by step solution

01

Understand the Equation

The equation given is in the form of a linear equation: \(y = -1\). This represents a horizontal line where the y-coordinate is constant and equal to -1.
02

Identify the Y-Intercept

The y-intercept of the line is the point where the line crosses the y-axis. In this equation, the y-intercept is -1, which means the line crosses the y-axis at the point (0, -1).
03

Draw a Horizontal Line

Since the equation describes a horizontal line where y is always -1, draw a straight, horizontal line that passes through the y-coordinate -1. This line is parallel to the x-axis.

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Key Concepts

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

Linear Equations
Linear equations are mathematical expressions that create straight lines when graphed. They typically have the form:
  • Standard form: Ax + By = C
  • Slope-intercept form: y = mx + b
  • Horizontal form: y = k
In the above problem, the equation is in the horizontal form, where the value of y is constant. Linear equations are defined by a degree of 1, meaning that highest power of the variable is 1. This simplicity ensures that the graph is always a straight line.
Y-Intercept
The y-intercept is a crucial concept when graphing linear equations. It is the point where the line crosses the y-axis. This is found by setting x to zero. For instance, in the equation y = -1, the line crosses the y-axis at (0, -1). Understand that this intercept determines part of the line's position on the graph. The y-intercept is often denoted by the letter 'b' in the slope-intercept form y = mx + b.
Horizontal Lines
Horizontal lines are special types of linear equations. They occur when the y-value is constant, regardless of the x-value. For example, the equation y = -1 means that no matter the value of x, y will always be -1. This results in a flat, horizontal line across the graph. To draw these lines:
  • Identify the constant y-value.
  • Draw a straight horizontal line through that y-value, parallel to the x-axis.
Horizontal lines are easy to recognize and draw as they have a slope of zero.

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Most popular questions from this chapter

A point \((x, y)\) has the property that \(x y>0 .\) In which quadrant(s) must the point lie? Explain.

Find the \(x\) -intercept and the \(y\) -intercept for the graph of each equation. $$ x-5=0 $$

Find each quotient. $$ \frac{5-(-7)}{-4-(-1)} $$

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ 5 y=-15 $$

Graph each linear equation. \(x-1=-4\)
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