Problem 13 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 13

Find the $x$ -intercept and the $y$ -intercept for the graph of each equation. $$ x-y=8 $$

Short Answer

Expert verified

x-intercept: (8,0), y-intercept: (0,-8)

Step by step solution

Find the x-intercept

Set y to 0 in the equation and solve for x. The x-intercept is where the graph crosses the x-axis.

Step 1.1: Substitute y=0

Substitute 0 for y in the equation: x - 0 = 8

Step 1.2: Solve for x

Simplify the equation to find x: x = 8

Find the y-intercept

Set x to 0 in the equation and solve for y. The y-intercept is where the graph crosses the y-axis.

Step 2.1: Substitute x=0

Substitute 0 for x in the equation: 0 - y = 8

Step 2.2: Solve for y

Simplify the equation to find y: -y = 8 *y = -8*

Conclusion: Identify the intercepts

The x-intercept is where the graph crosses the x-axis, and the y-intercept is where it crosses the y-axis. Using the previous steps: x-intercept: (8,0) y-intercept: (0,-8)

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Key Concepts

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

x-intercept

In algebra, the x-intercept of a graph is the point where it crosses the x-axis. To find the x-intercept, we set the value of y to 0 and solve for x.

For example, let's look at the equation given in the exercise:

$x - y = 8$

Step 1: Set y to 0.

This transforms the equation to:

$x - 0 = 8$

Step 2: Solve for x.

This simplifies to:

$x = 8$

Hence, the x-intercept is the point (8, 0). This means the graph crosses the x-axis at the coordinate (8, 0).

Understanding this helps us know where the graph begins horizontally when plotting points.

y-intercept

The y-intercept of a graph is the point where it crosses the y-axis. To find the y-intercept, we set the value of x to 0 and solve for y.

Using the same equation:

$x - y = 8$

Step 1: Set x to 0.

Doing so changes the equation to:

$0 - y = 8$

Step 2: Solve for y.

We get:

$-y = 8$

Divide by -1:

$y = -8$

Therefore, the y-intercept is the point (0, -8). This indicates that the graph crosses the y-axis at the coordinate (0, -8).

This understanding lets us know where the graph starts vertically.

solving equations

Solving equations is a fundamental part of finding intercepts. It involves finding the variable's value that makes the equation true.

Here are the basic steps we follow to solve for a variable:

Substitute any known values: In our intercept problems, we substitute either x=0 or y=0.
Simplify the equation: This often means performing basic arithmetic operations.
Isolate the variable: Do this by getting the variable by itself on one side of the equation.

For instance, substituting y=0 in the equation $x - y = 8$ simplifies to $x = 8$. Similarly, substituting x=0 simplifies to solving $-y = 8$, which gives us y = -8.

Knowing how to solve equations helps reveal graph intersections clearly and is a valuable tool for various math problems beyond just finding intercepts.

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91影视

Find the \(x\) -intercept and the \(y\) -intercept for the graph of each equation. $$ x-y=8 $$

Short Answer

Step by step solution

Find the x-intercept

Step 1.1: Substitute y=0

Step 1.2: Solve for x

Find the y-intercept

Step 2.1: Substitute x=0

Step 2.2: Solve for y

Conclusion: Identify the intercepts

Key Concepts

x-intercept

y-intercept

solving equations

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