Problem 26 Find the $x$ -intercept and th... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 3: Problem 26

Find the $x$ -intercept and the $y$ -intercept for the graph of each equation. $$ x-5=0 $$

Short Answer

Expert verified

The x-intercept is (5, 0) and there is no y-intercept.

Step by step solution

Identify the Equation

The given equation is a simple linear equation: \[ x - 5 = 0 \]

Solve for the x-intercept

To find the x-intercept, set $ y = 0 $ and solve for $ x $. For this equation, there is no $ y $ term, so we solve for $ x $ directly. \[ x - 5 = 0 \]Add 5 to both sides: \[ x = 5 \]Thus, the x-intercept is at $ (5, 0) $.

Determine the y-intercept

To find the y-intercept, set $ x = 0 $ and solve for $ y $. Since there is no $ y $ term in the equation $ x - 5 = 0 $, this equation does not intercept the y-axis. Every point on this line has a constant x-value of 5, and there is no corresponding $ y $ value that will satisfy $ x = 0 $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

x-intercept

In linear equations, the x-intercept is found where the graph crosses the x-axis. To determine the x-intercept, set the value of y to 0 and solve for x. This is because any point on the x-axis has a y value of 0. In our example equation: \[ x - 5 = 0 \] we solve for x to get \[ x = 5 \] Therefore, the x-intercept is at the point (5, 0). This means that the graph of the equation intersects the x-axis at x = 5.

y-intercept

The y-intercept is where the graph of an equation crosses the y-axis. To find the y-intercept, set x to 0 and solve for y. This is done because any point on the y-axis has an x value of 0. In our example equation: \[ x - 5 = 0 \] there isn鈥檛 a y term present. Because of this, the equation cannot intersect the y-axis. Solving for y is impossible in this case as no value of y will make x equal to 0. Thus, this equation does not have a y-intercept.

linear equations

Linear equations are equations of the first degree. They form a straight line when graphed. The general form of a linear equation is \[ ax + by = c \] where a, b, and c are constants.

When graphed, the solutions to the equation form a line.
These lines can have x-intercepts, y-intercepts, or both depending on their slope and position.

In our example, the equation \[ x - 5 = 0 \] simplifies to \[ x = 5 \], indicating a vertical line crossing the x-axis at 5. The curves or lines from linear equations are essential in various applications, such as physics, economics, and engineering.

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91影视

Find the \(x\) -intercept and the \(y\) -intercept for the graph of each equation. $$ x-5=0 $$

Short Answer

Step by step solution

Identify the Equation

Solve for the x-intercept

Determine the y-intercept

Key Concepts

x-intercept

y-intercept

linear equations

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