Problem 9 Find the $x$ - and $y$ -inte... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 3: Problem 9

Find the $x$ - and $y$ -intercepts. $$ x-y=3 $$

Short Answer

Expert verified

The x-intercept is $(3, 0)$ and the y-intercept is $(0, -3)$.

Step by step solution

Find the x-intercept

To find the x-intercept, set $ y = 0 $ in the equation and solve for $ x $. \[ x - 0 = 3 \] Simplifying gives $ x = 3 $. Thus, the x-intercept is the point $ (3, 0) $.

Find the y-intercept

To find the y-intercept, set $ x = 0 $ in the equation and solve for $ y $. \[ 0 - y = 3 \] Simplifying gives $ y = -3 $. Thus, the y-intercept is the point $ (0, -3) $.

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Key Concepts

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

x-intercept

The concept of the x-intercept is crucial when learning about linear equations. The x-intercept refers to the point where the graph of an equation crosses the x-axis. At this point, the y-coordinate is always zero. To find the x-intercept of an equation, you need to set the y-value to zero and solve for the x variable.
For example, consider the linear equation $x - y = 3$. To find its x-intercept:

Set $y = 0$ in the equation: $x - 0 = 3$.
Solve for $x$: Simplifying gives $x = 3$.
This means the x-intercept occurs at the point $(3, 0)$.

Whenever you are given a linear equation, finding the x-intercept helps you understand how the line interacts with the x-axis. It is a straightforward process that requires only simple substitution and solving.

y-intercept

Just like the x-intercept, the y-intercept is an essential part of understanding linear equations. The y-intercept is the point where the graph of an equation crosses the y-axis. At this point, the x-coordinate is zero. To find the y-intercept of an equation, set the x-value to zero and solve for y.
For instance, in the linear equation $x - y = 3$, to find its y-intercept:

Set $x = 0$ in the equation: $0 - y = 3$.
Solve for $y$: Simplifying gives $y = -3$.
This indicates the y-intercept occurs at the point $(0, -3)$.

Finding the y-intercept is integral to grasping the behavior of a line on a graph. It gives a clear indication of where the line will cut across the y-axis, helping to understand the linear relationship between the variables.

solving equations

Solving equations is a fundamental concept in algebra that involves finding the value of unknown variables that satisfy the equation. Whether we are looking for x-intercepts, y-intercepts, or simply solving for a variable, the process typically involves manipulation and simple arithmetic.
Here's a useful approach:

Identify what you are solving for (e.g., x or y).
Arrange the equation to isolate the desired variable on one side of the equation.
Use arithmetic operations such as addition, subtraction, multiplication, or division systematically to solve for the variable.

In our given example $x - y = 3$, finding intercepts required solving equations:

For the x-intercept, solve $x = 3$ with $y = 0$.
For the y-intercept, solve $y = -3$ with $x = 0$.

This simple problem-solving skill is essential not just for intercepts but for various areas of algebra and mathematics. Mastery of this concept will significantly enhance your ability to tackle more complex equations and mathematical challenges.

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91影视

Find the \(x\) - and \(y\) -intercepts. $$ x-y=3 $$

Short Answer

Step by step solution

Find the x-intercept

Find the y-intercept

Key Concepts

x-intercept

y-intercept

solving equations

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