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.
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.
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.