/*! 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 94 Find the \(x\) -intercept and th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 94

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. $$y=-2 x+16$$

Short Answer

Expert verified
The x-intercept of the graph is \(x=8\) and the y-intercept of the graph is \(y=16\).

Step by step solution

01

Find the x-intercept

Set \(y = 0\) in the equation and solve for \(x\). This gives the equation \(0=-2x+16\). If you solve it, this leads to \(x=8\). Therefore, the x-intercept is \(x = 8\).
02

Find the y-intercept

Set \(x = 0\) in the equation and solve for \(y\). This gives the equation \(y=-2*0+16\). The answer is \(y = 16\). Therefore, the y-intercept is \(y = 16\).

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 concept of the x-intercept is quite fundamental when working with linear equations. To determine where a line crosses the x-axis, we set the value of \( y \) to zero.
Let's look at the equation from the exercise: \( y = -2x + 16 \).
By placing \( 0 \) for \( y \), you get the equation \( 0 = -2x + 16 \). To isolate \( x \), you solve the equation:
  • First, move \( 16 \) to the other side by subtracting 16 from both sides, resulting in \( -16 = -2x \).
  • Then, divide both sides by \(-2\) to solve for \( x \). This gives \( x = 8 \).
The x-intercept is the point \((8, 0)\), indicative of where the line graph meets the x-axis on a coordinate plane.
Exploring the Y-Intercept
Finding the y-intercept involves a similar process but in reverse. This is where the line intersects the y-axis. To find it, set \( x = 0 \) and solve for \( y \).
Using the exercise's equation, \( y = -2x + 16 \), substitute \( 0 \) for \( x \), leaving \( y = -2(0) + 16 \).
Because multiplying by zero results in zero, the calculation simplifies to \( y = 16 \).
Thus, the y-intercept is at the point \((0, 16)\).
  • This point shows precisely where the graph intersects the y-axis.
  • Having both intercepts is crucial for graphing a line on a coordinate plane.
Graphing Linear Equations
Graphing a linear equation like \( y = -2x + 16 \) requires understanding of both intercepts. They are crucial points of reference. With the x-intercept \((8, 0)\) and the y-intercept \((0, 16)\), you can plot these points on a coordinate plane to visually represent the equation.
After plotting, simply draw a straight line through these points. This line embodies all solutions of the equation.
Key points to remember:
  • Linear equations form straight lines on graphs. Knowing the intercepts provides straightforward points to draw from.
  • A graph can give a quick insight into how variables relate visually, offering a clearer understanding of the equation's behavior.
  • Intercepts are not just numbers; they are coordinates that guide your graphing process.
Finding and using intercepts are fundamental tasks in graphing linear equations taught in algebra.

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

You start a daily flower club and charge \(\$ 10\) to join and \(\$ .50\) per day. Every day each member of the club gets a fresh flower. Let \(n\) represent the number of club members and let \(I\) represent your income for four weeks. A model for the situation is \(I=[10+4 \cdot 7(0.5)] n .\) Write an input-output table that shows your income for \(2,4,6,8,\) and 10 club members.

Find the sum or the difference of the matrices. $$ \left[\begin{array}{rr}4 & -8 \\\7 & 0\end{array}\right]-\left[\begin{array}{rr}-5 & 3 \\\\-5 & -7\end{array}\right] $$

find the quotient. $$ 54 \div 9 $$

Decide whether the given point lies on the line. Justify your answer both algebraically and graphically. $$x-y=10 ;(5,-5)$$

Find the value of \(y\) so that the line passing \((2,-15),(5, y), m=\frac{4}{5}\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.