/*! 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 36 Write each equation in slope-int... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 36

Write each equation in slope-intercept form and identify the slope and y-intercept of the line. $$2 x-2 y=1$$

Short Answer

Expert verified
The slope is 1 and the y-intercept is -\frac{1}{2}.

Step by step solution

01

- Write the Equation

Start with the given equation: \[ 2x - 2y = 1 \]
02

- Rearrange to Isolate y

To write the equation in slope-intercept form, the goal is to isolate y. First, subtract 2x from both sides: \[ -2y = -2x + 1 \]
03

- Divide by the Coefficient of y

Divide every term by -2 to solve for y: \[ y = x - \frac{1}{2} \] Now, the equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
04

- Identify the Slope and y-Intercept

From the slope-intercept form of the equation \( y = x - \frac{1}{2} \), identify the slope (\( m \)) and the y-intercept (\( b \)): \( m = 1 \) \( b = -\frac{1}{2} \)

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.

Linear Equations
A linear equation is a fundamental concept in algebra. It represents a straight line on a graph. A typical linear equation looks like this:
  • ax + by = cHosted by a plot, this equation shows how one variable (usually y) depends on another variable (often x).
To make the relationship more explicit, we often rewrite it in a different form called the slope-intercept form.
Slope
Slope measures the steepness of a line. It tells us how much y changes for a unit change in x. In the slope-intercept form of a linear equation, written as y = mx + b, the slope is represented by 'm'.
  • If m is positive, the line slopes upwards.
  • If m is negative, the line slopes downwards.
  • A larger value of m means a steeper slope.
For the provided equation, 2x - 2y = 1, after converting to slope-intercept form, we get y = x - 陆, where the slope (m) is 1. This means for every unit increase in x, y increases by 1.
Y-intercept
The y-intercept is the point where the line crosses the y-axis. It's represented by 'b' in the slope-intercept form y = mx + b. When x equals 0, the result for y will be the y-intercept. In our example, the equation y = x - 陆 has a y-intercept of -陆. This means when x is 0, y will be -陆. Understanding the y-intercept helps in quickly sketching the graph of the equation.
Algebra
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. It is about finding the values of unknowns. By understanding concepts like linear equations, slopes, and y-intercepts, you can solve for unknowns and graph linear equations effectively. For our example, starting with 2x - 2y = 1, we use algebraic manipulations to bring it to the form y = mx + b, allowing us to easily identify the slope and y-intercept and create a graph. This practice is crucial for mastering algebra and its applications in various mathematical problems.

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

Solve \(x^{2}+2 x=9\).

Solve each equation. $$\frac{y-1}{y+4}=\frac{y+1}{y-2}$$

Maximum Girth United Parcel Service (UPS) defines girth of a box as the sum of the length, twice the width, and twice the height. The maximum length that can be shipped with UPS is 108 in. and the maximum girth is 130 in. If a box has a length of 40 in. and a width of 30 in. then in what range must the height fall?

Recall that \(\sqrt{w}\) is a real number only if \(w \geq 0\) and \(1 / w\) is a real mumber only if \(w \neq 0 .\) For what values of \(x\) is each of the following expressions a real mumber? $$\frac{5}{\sqrt{3-2 x}}$$

Solve each equation. $$x-0.05 x=190$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.