/*! 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 101 An equation is \(y=\frac{3}{4} x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 101

An equation is \(y=\frac{3}{4} x-9 .\) Find \(y\) when \(x=8\).

Short Answer

Expert verified
When \( x = 8 \), \( y = -3 \).

Step by step solution

01

Identify the equation and given value

The equation provided is \( y = \frac{3}{4} x - 9 \). The value given for \( x \) is 8.
02

Substitute the given value into the equation

Replace \( x \) with 8 in the equation: \( y = \frac{3}{4}(8) - 9 \).
03

Calculate the product

Multiply \( \frac{3}{4} \) by 8: \( \frac{3}{4} \times 8 = 6 \). So, the equation now is \( y = 6 - 9 \).
04

Solve for y

Subtract 9 from 6: \( y = 6 - 9 = -3 \).

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.

Solving for y
To solve for \(y\), we need to isolate it on one side of the equation. Start with the given equation: \(y = \frac{3}{4}x - 9\). When we have information about \(x\), we substitute it into the equation, making it possible to directly calculate \(y\). In our case, \(x = 8\). To begin, we substitute 8 for \(x\) in the equation: \[ y = \frac{3}{4} (8) - 9 \]. This substitution sets the stage for further algebraic operations and lets us find the value of \(y\).
Substitution Method
The substitution method is a vital technique in algebra. It involves replacing a variable with a given number or expression. In our exercise, after identifying the equation \(y = \frac{3}{4}x - 9\), the next step is to replace \(x\) with 8. This is done as follows: \[ y = \frac{3}{4} \cdot 8 - 9 \]. Substitution simplifies the equation, transforming it into a simpler problem where \(y\) depends solely on numerical values. This method is particularly useful in solving systems of equations or evaluating functions at specific points.
Evaluating Expressions
Evaluating expressions means calculating the value of an algebraic expression by substituting values for the variables within it. Let's take our substituted equation: \[ y = \frac{3}{4} \cdot 8 - 9 \]. We first multiply the fraction by 8: \[ \frac{3}{4} \cdot 8 = 6 \]. This transforms the equation to a simpler form: \[ y = 6 - 9 \]. From here, we further simplify to find the value of \(y\). This step-by-step evaluation clarifies the process and helps in understanding how changes in one part of the equation affect the whole.
Algebraic Operations
Algebraic operations are the methods we use to manipulate equations and expressions. They include operations like addition, subtraction, multiplication, and division. In our exercise, once we substituted \(x\) with 8, we proceeded with multiplication: \[ \frac{3}{4} \cdot 8 = 6 \]. This step involves fractions and shows how to handle different types of numbers in calculations. Finally, we performed subtraction: \[ 6 - 9 = -3 \], resulting in \(y = -3\). Mastering these operations is essential for solving equations accurately and efficiently.

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

(a) graph the given points, and draw a line through the points. (b) use the graph to find the slope of the line. (c) use the slope formula to find the slope of the line. \((-30,-40) ;(10,30)\)

(a) write the equation of the vertical line that passes through the point. (b) graph the equation. \((-2,-1)\)

(a) write the equation of the vertical line that passes through the point. (b) graph the equation. \((6,3)\)

(a) graph the given points, and draw a line through the points. (b) use the graph to find the slope of the line. (c) use the slope formula to find the slope of the line. \((0,-7) ;(3,0)\)

(a) graph the given points, and draw a line through the points. (b) use the graph to find the slope of the line. (c) use the slope formula to find the slope of the line. \((-3,-4) ;(1,3)\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Calculus

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.