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Chapter 2: Problem 7

A \(y\) -intercept of a graph has an \(x\) -coordinate of _____ .

Short Answer

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Step by step solution

01

Understanding the y-intercept

The y-intercept of a graph is the point where the graph intersects the y-axis.
02

Coordinate of y-intercept

At the y-intercept, the x-coordinate is always 0 because it lies on the y-axis where the value of x does not deviate from zero.
03

Conclusion

Thus, the x-coordinate of the y-intercept is 0.

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Key Concepts

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

x-coordinate
The x-coordinate is one part of a pair of numbers that defines a point on the coordinate plane. It tells you how far to move horizontally from the origin (0,0). In the case of the y-intercept, the x-coordinate is always 0. This is because the y-intercept is where the graph crosses the y-axis.

The y-axis itself is the vertical line where the value of x is always zero. Consequently, any point on the y-axis will have an x-coordinate of 0. For example, if a graph crosses the y-axis at (0, 5), the x-coordinate is 0.
graph
A graph is a visual representation of equations or data points plotted on a coordinate system. The two main components of a graph are the x-axis (horizontal axis) and the y-axis (vertical axis).

Each point on the graph represents a pair of values, known as coordinates \((x, y)\). The x-coordinate represents the horizontal position, while the y-coordinate represents the vertical position.

Graphs are helpful for understanding the relationship between variables in mathematical equations, making patterns in data easier to recognize. For example, the graph of a linear equation (a straight line) can show us how changes in one variable affect another.
y-axis
The y-axis is the vertical line on a graph. It is one of the two axes in the Cartesian coordinate system, with the other being the x-axis.

The y-axis is essential for identifying the y-coordinate of a point, which shows how far up or down the point is from the origin (0,0).

One key feature of the y-axis is the y-intercept. This is the point where the graph crosses the y-axis, and at this point, the x-coordinate is always 0. For instance, in the equation y = 3x + 2, when x is 0, y is 2. So, the y-intercept is (0, 2). Understanding the y-axis helps in graphing functions and interpreting data.

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