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

Verified step by step guidance

1. To find the x-intercept of the equation, set \( y = 0 \) and solve for \( x \).
2. Substitute \( y = 0 \) into the equation: \( 2x + 5(0) = 10 \).
3. Simplify the equation: \( 2x = 10 \).
4. Divide both sides by 2 to solve for \( x \): \( x = \frac{10}{2} \).
5. The x-intercept is the point where the graph crosses the x-axis, which is \( (x, 0) \).

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It typically takes the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear equations is essential for finding intercepts, as they define the relationship between x and y values.

X-Intercept

The x-intercept of a graph is the point where the graph crosses the x-axis, which occurs when the value of y is zero. To find the x-intercept, you set y to zero in the equation and solve for x. This concept is crucial for understanding how to analyze and interpret the behavior of linear functions.

Solving for Variables

Solving for variables involves manipulating an equation to isolate a specific variable, allowing you to determine its value. In the context of finding the x-intercept, this means substituting y = 0 into the equation and rearranging it to solve for x. Mastery of this skill is fundamental in algebra for analyzing equations and their graphs.