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Chapter 2: Problem 53

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ x=2 $$

Short Answer

Expert verified
The x-intercept is (2,0). There is no y-intercept.

Step by step solution

01

Determine the x-intercept

To find the x-intercept, set y=0 and solve for x. Since the equation is given as \(x=2\), the x-intercept is \(x=2\). Therefore, the x-intercept is the point (2,0).
02

Determine the y-intercept

To find the y-intercept, set x=0 and solve for y. In the equation \(x=2\), there is no value of y that makes x equal to zero. Therefore, the equation \(x=2\) does not intersect the y-axis, and there is no y-intercept.
03

Graph the equation

To graph \(x=2\), draw a vertical line that passes through x=2 on the x-axis. This line is parallel to the y-axis.

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Key Concepts

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

Graphing Linear Equations
Linear equations represent straight lines on a coordinate plane and can be graphed using their intercepts, slope, or plotting points. The general form of a linear equation is given by: \[ y = mx + b \] where\(m\) is the slope and \(b\) is the y-intercept.
Finding X-Intercepts
The x-intercept of a graph is the point where the line crosses the x-axis. This occurs when the y-value is zero. To find the x-intercept, set y equal to zero in the equation and solve for x. For example, in the equation \(x=2\), you can see that when y is set to zero, the x-value remains 2. Hence, the x-intercept is at \((2, 0)\).
Finding Y-Intercepts
The y-intercept of a graph is the point where the line crosses the y-axis. This happens when the x-value is zero. To find the y-intercept, set x equal to zero in the equation and solve for y. However, for the equation \(x=2\), there is no y-value that makes x equal to zero. Hence, there is no y-intercept for this equation.
Vertical Lines in Graphing
A vertical line is represented by an equation of the form \(x=a\), where \(a\) is a constant. This line runs parallel to the y-axis and crosses the x-axis at the point \(a\). For our equation \(x=2\), the graph is a vertical line that passes through \(x=2\) on the x-axis. It's important to note that a vertical line, such as \(x=2\), does not have a y-intercept because it never crosses the y-axis.

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Most popular questions from this chapter

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