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Chapter 3: Problem 44

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ y=-3 $$

Short Answer

Expert verified
The y-intercept is (0, -3) and there is no x-intercept. The graph is a horizontal line at y = -3.

Step by step solution

01

Identify the y-intercept

The y-intercept is the point where the graph crosses the y-axis. For the equation \(y = -3\), the graph is a horizontal line at \(y = -3\). Thus, the y-intercept is \((0, -3)\).
02

Identify the x-intercept

The x-intercept is the point where the graph crosses the x-axis. Since the graph of \(y = -3\) is a horizontal line and it does not cross the x-axis, there is no x-intercept.
03

Graph the equation

To graph the equation \(y = -3\), draw a horizontal line that passes through the point \( (0, -3) \). This line extends infinitely to the left and right.

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Key Concepts

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

x-intercepts
The x-intercept of a graph is a point where the graph crosses the x-axis. At this point, the value of y is zero. To find the x-intercept of an equation, you set y equal to zero and solve for x. However, in the case of the equation \(y = -3\), the line is horizontal and does not touch the x-axis, so there are no x-intercepts. This is typical for horizontal lines unless they lie on the x-axis.
y-intercepts
The y-intercept is where the graph crosses the y-axis. At this point, the value of x is zero. For the equation \(y = -3\), you can find the y-intercept by setting x to zero and solving for y. In this case, it鈥檚 already solved for y, so the y-intercept is \( (0, -3)\). To identify this point on the graph, locate the y-axis and find the point where y is -3.
horizontal lines
Horizontal lines have a constant y-value for every x-value. The equation \(y = -3\) represents a horizontal line because y does not change regardless of the value of x. This line passes through all points with a y-coordinate of -3 and extends infinitely to the left and right. When graphing a horizontal line, ensure it remains perfectly parallel to the x-axis.
coordinate plane
The coordinate plane is a two-dimensional surface formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis. Each point on the plane is described by a pair of coordinates, (x, y). The center of the coordinate plane, where the x-axis and y-axis intersect, is called the origin, noted as (0,0). In the exercise, the point (0, -3) is significant because it is the y-intercept and lies on the y-axis. Understanding how to plot points on the coordinate plane is essential for graphing linear equations accurately.

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Most popular questions from this chapter

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