/*! 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 32 Indicate which of the given orde... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 32

Indicate which of the given ordered pairs are solutions for each equation. $$y=-3 x+2 \quad(0,-3),(0,2),(-3,0)$$

Short Answer

Expert verified
The ordered pair (0, 2) is the solution for the equation.

Step by step solution

01

Understand the Equation

The given equation is \( y = -3x + 2 \), which represents a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. We need to determine whether each ordered pair satisfies this equation.
02

Analyze the Ordered Pair (0, -3)

Substitute \( x = 0 \) and \( y = -3 \) into the equation: \( -3 = -3(0) + 2 \). Simplifying gives \( -3 = 2 \), which is false. Therefore, the pair (0, -3) is not a solution.
03

Analyze the Ordered Pair (0, 2)

Substitute \( x = 0 \) and \( y = 2 \) into the equation: \( 2 = -3(0) + 2 \). Simplifying gives \( 2 = 2 \), which is true. Therefore, the pair (0, 2) is a solution.
04

Analyze the Ordered Pair (-3, 0)

Substitute \( x = -3 \) and \( y = 0 \) into the equation: \( 0 = -3(-3) + 2 \). Simplifying gives \( 0 = 9 + 2 \) or \( 0 = 11 \), which is false. Therefore, the pair (-3, 0) is not a solution.
05

Determine the Valid Solutions

Based on the calculations, (0, 2) is the only ordered pair that satisfies the equation \( y = -3x + 2 \).

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.

Slope-Intercept Form
Linear equations are often represented in what is known as the slope-intercept form. This form is written as \( y = mx + b \), where:
  • \( m \) represents the slope of the line.
  • \( b \) is the y-intercept, indicating where the line crosses the y-axis.
For our specific equation \( y = -3x + 2 \), the slope \( m \) is \(-3\), meaning the line descends or moves downward by 3 units for every 1 unit it moves to the right. The y-intercept \( b \) is 2, so the line crosses the y-axis at the point (0, 2).
The slope-intercept form gives us a clear picture of how the line behaves on a graph without plotting multiple points. By knowing just the slope and the y-intercept, we can quickly draw and understand the line's position and direction.
Understanding Ordered Pairs
Ordered pairs are crucial in determining the location of points on a graph. Each ordered pair consists of an \( x \)-coordinate and a \( y \)-coordinate, represented in the format \((x, y)\).
In the exercise, we are tasked with finding out if given ordered pairs are solutions to the linear equation \( y = -3x + 2 \). This means we're checking if when we plug in these \( x \) and \( y \) values into the equation, both sides of the equation are equal or true.
  • For example, with the pair (0, 2): substituting \( x = 0\) and \( y = 2\) verifies the equation because \(2 = 2\).
  • However, with the pair (0, -3), substituting \( x = 0\) and \( y = -3\) gives \(-3 = 2\), which is incorrect.
Evaluating ordered pairs in this manner helps confirm which points lie on the graph of the equation.
Solution Verification
Solution verification is the process of confirming that a particular ordered pair satisfies the given equation. It involves substituting the \( x \) and \( y \) values from the pair into the equation and checking if the equation holds true.
For the linear equation \( y = -3x + 2 \), let's see how verification works:
  • If substituting an ordered pair results in both sides of the equation being equal, the pair is a valid solution, meaning it lies on the line described by the equation.
  • If the results do not match, the ordered pair is not a solution and does not lie on the line.
In our task, (0, 2) verifies as a solution because substituting \( x \) and \( y \) gives \( 2 = 2 \). The others do not verify because when substituted, the equalities do not hold true. Solution verification is a key step in problems involving graphing and understanding linear equations, ensuring accuracy and deeper insight into the equation's nature.

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

Add or subtract as indicated. $$\frac{2}{5}-\frac{5}{10}$$

Find the reciprocal of each number. $$3$$

Add or subtract as indicated. $$\frac{x}{8}-\frac{5}{6}$$

Suppose \(4 x+3 y=12 .\) Find \(x\) if: $$y=-3$$

Rectangle \(A B C D\) has a length of 5 and a width of \(3 .\) Point \(D\) is the ordered pair \((-1,1)\). Find points \(A, B,\) and \(C\) (GRAPH CANT COPY)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.