Problem 66
Question
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.
Step-by-Step Solution
Verified Answer
The statement is true. The graph of a linear equation can have either no \(x\)-intercept or only one \(x\)-intercept.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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.
Other exercises in this chapter
Problem 66
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