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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
Chapter 3, Problem 5

Fill in the blank to correctly complete each sentence. The x-intercept of the graph of 2x + 5y = 10 is ________.

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Recall that the x-intercept of a graph is the point where the graph crosses the x-axis. At this point, the value of y is 0.
To find the x-intercept, substitute y = 0 into the equation of the line: \(2x + 5(0) = 10\).
Simplify the equation after substitution: \(2x = 10\).
Solve for x by dividing both sides of the equation by 2: \(x = \frac{10}{2}\).
The x-intercept is the point where \(x\) equals this value and \(y = 0\), so the x-intercept is \((x, 0)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding x-intercepts

The x-intercept of a graph is the point where the graph crosses the x-axis. At this point, the value of y is always zero. To find the x-intercept, set y = 0 in the equation and solve for x.
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Solving linear equations

Solving linear equations involves isolating the variable to find its value. In this context, after substituting y = 0, you solve the resulting equation for x to determine the x-intercept.
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Standard form of a linear equation

A linear equation in two variables is often written in standard form as Ax + By = C. Understanding this form helps identify coefficients and constants, making it easier to manipulate the equation to find intercepts.
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