Problem 90 Find the $x$ -intercept and th... [FREE SOLUTION]

Chapter 4: Problem 90

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

Short Answer

Expert verified

The y-intercept is 8 and the x-intercept is -8.

Step by step solution

Identify y-intercept

To identify the y-intercept, set $x = 0$ in the given equation $y = x + 8$. Replacement of $x$ yields, $y = 0 + 8 = 8$. Thus, the y-intercept is 8.

Identify x-intercept

To identify the x-intercept, set $y = 0$ in the given equation $y = x+8$. Replacement of $y$ gives $0 = x + 8$. Solving this equation, we get, $x= -8$. Thus the x-intercept is -8.

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Key Concepts

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

Understanding the x-intercept

When we talk about the x-intercept of a linear equation, we are referring to the point where the graph of the equation crosses the x-axis. This is the point where the value of the y-coordinate is zero because any point on the x-axis has a y-value of 0.
To find the x-intercept, you follow a straightforward method:

Set the y value of the equation to 0.
Solve for x, the remaining variable.

In the context of our example equation, which is given as $ y = x + 8 $, we set $y = 0$. This gives us the equation $0 = x + 8$. Solving for $x$, we subtract 8 from both sides to get $x = -8$. Therefore, the x-intercept is at the point (-8, 0). This tells us exactly where the graph crosses the x-axis.

Exploring the y-intercept

A y-intercept of a linear equation is where the graph of the line crosses the y-axis. At this point, the value of x is zero because all points on the y-axis have x-values of 0.
To determine the y-intercept, the procedure is similarly direct:

Set the x value in the equation to 0.
Solve for y.

For the equation $y = x + 8$, we substitute $x = 0$. This results in $y = 0 + 8$, which simplifies to $y = 8$. Therefore, the y-intercept is at the point (0, 8).
This point indicates where the line will cross the y-axis, providing a key point for graphing the equation.

Basic principles of solving linear equations

Solving linear equations involves finding the values of the variables that satisfy the equation. A linear equation typically looks like $ y = mx + b $, where $m$ and $b$ are constants.
When solving, the goals are:

Isolate the variable.
Use basic arithmetic operations, like addition or subtraction, to simplify the equation.

For the example equation $y = x + 8$, we solve for the intercepts by isolating either x or y. Solving the equation by setting $y = 0$ gives the x-intercept, and setting $x = 0$ gives the y-intercept.
Understanding the intercepts is fundamental, as they provide critical points to sketch the line on a graph, helping to visualize the relationship between x and y.

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91影视

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

Short Answer

Step by step solution

Identify y-intercept

Identify x-intercept

Key Concepts

Understanding the x-intercept

Exploring the y-intercept

Basic principles of solving linear equations

One App. One Place for Learning.

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