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Chapter 1: Problem 66

Determine whether the statement is true or false. Justify your answer. The graph of a linear equation can have either no \(x\) -intercepts or only one \(x\) -intercept.

Short Answer

Expert verified
The statement is true. The graph of a linear equation can have either no \(x\)-intercept or only one \(x\)-intercept.

Step by step solution

01

Understand Linear Equations and \(x\)-intercepts

A linear equation is an equation that has a graph in the shape of a straight line. An \(x\)-intercept of a graph is the point or points at which the graph intersects the \(x\)-axis.
02

Consider the characteristics of a linear equation

Linear equations will generally have the form \(y = mx + c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. You can confirm that the equation is linear if it can be written in this form.
03

Apply knowledge to the statement

The graph of a linear equation can have one \(x\)-intercept if it crosses the \(x\)-axis at one point. Or, it could have no \(x\)-intercept at all if the line is parallel to the \(x\)-axis. Therefore, it is true that the graph of a linear equation can have either no \(x\)-intercept or only one \(x\)-intercept.

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Most popular questions from this chapter

Proof Prove that if \(f\) and \(g\) are one-to-one functions, then \((f \circ g)^{-1}(x)=\left(g^{-1} \circ f^{-1}\right)(x)\).

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