/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 91 Find the \(x\) -intercept and th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 91

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. $$y=2 x+12$$

Short Answer

Expert verified
The x-intercept of the graph is \(-6, 0\) and the y-intercept is \(0, 12\).

Step by step solution

01

Find the x-intercept

Set \(y = 0\) in the equation and solve for \(x\). Doing this gives us: \(0=2x + 12\).
02

Solve for x

Solve the equation \(0=2x + 12\) by subtracting 12 from both sides to get \(2x = -12\). Then, divide by 2, yielding \(x = -6\). Therefore, the coordinate of the x-intercept is \(-6, 0\).
03

Find the y-intercept

The y-intercept is where \(x = 0\). Substitute \(x = 0\) into the equation to get \(y = 2(0) + 12\).
04

Solve for y

Solving the equation \(y = 2(0) + 12\), gives \(y = 12\). Therefore, the coordinate of the y-intercept is \(0, 12\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding the X-Intercept
The x-intercept is an important concept in the graph of a linear equation. It is the point where the graph of the equation crosses the x-axis. To find the x-intercept, we need to understand that at this point, the value of the y-coordinate is always zero. This is because any point on the x-axis has a y-value of zero.

To calculate the x-intercept for the equation given in the exercise, set y equal to zero and solve for x.
  • Start with the equation: \(0 = 2x + 12\).
  • Solve by isolating x: subtract 12 from both sides, resulting in \(2x = -12\).
  • Finally, divide both sides by 2, giving \(x = -6\).
Thus, the coordinate of the x-intercept for this given equation is \((-6, 0)\). This point tells us where the line representing the equation will touch or intersect with the x-axis, an essential step when graphing the equation.
Understanding the Y-Intercept
The y-intercept is another fundamental aspect of the graph of a linear equation. It is the point where the line crosses the y-axis. To find this point, we set the x-coordinate to zero. This works because any point on the y-axis has an x-value of zero.

To find the y-intercept for the equation in the example, substitute x with zero and solve for y:
  • Use the equation: \(y = 2(0) + 12\).
  • Simplify to find \(y = 12\).
Hence, the y-intercept for the equation \(y = 2x + 12\) is \((0, 12)\). This point tells us where the line will intersect with the y-axis, which is crucial for sketching the graph.
Exploring the Coordinate System
A coordinate system is a framework used to visually represent points in two dimensions, using a pair of numbers. These numbers are known as coordinates and are typically formatted as \((x, y)\). The x-axis runs horizontally, while the y-axis runs vertically.

Understanding the coordinate system is key when discussing concepts like x-intercepts and y-intercepts. Each intercept is a point where the line of an equation meets one of these axes. In the provided exercise:
  • The x-intercept \((-6, 0)\) means the line crosses the x-axis at x = -6 with zero height on the y-axis.
  • The y-intercept \((0, 12)\) means the line crosses the y-axis at height 12 with zero width on the x-axis.
The intersection points and plotting them on a grid is how one starts to sketch the equation鈥檚 line. Seeing these intercepts clearly on the coordinate plane aids in understanding how linear equations behave visually.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Apply the distributive property. $$-8(8-y)$$

Evaluate the expression for the given value of the variable. (Review 1.3 and 2.5 for 4.2 ) $$-3 x-9 y \text { when } x=-2 \text { and } y=-1$$

Plot and label the points \(R(2,4), S(0,-1), T(3,6),\) and \(U(-1,-2)\) in a coordinate plane.

Is the given number a solution of the inequality? $$3 x-11 \geq 2 ; 4$$

Apply the distributive property. $$-5 w(-3+2 w)$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.