/*! 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 61 Graph each equation using any me... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 61

Graph each equation using any method. $$y+2=\frac{3}{4}(4 x+8)$$

Short Answer

Expert verified
The graph of the equation \(y+2=\frac{3}{4}(4 x+8)\) is a straight line with a slope of 3 and y-intercept of 4.

Step by step solution

01

Simplify

Simplify the right side of equation: \(y+2=\frac{3}{4}(4 x+8)\) to get \(y+2 = 3x +6\).
02

Rearrange to slope-intercept form

It is easier to graph the equation once it's in the form \(y = mx+b\), which is the slope-intercept form. By doing that, we get the equation to be \(y = 3x + 4\). Here, the slope \(m\) = 3 and y-intercept \(b\) = 4.
03

Draw the graph

First, plot the y-intercept at (0,4) on the y-axis. The slope 3 means 'rise over run', as from each point on the line, you can go up 3 units and 1 unit to the right to get to the next point on the line. Draw these points and connect them to draw the line representing the given equation.

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
The slope-intercept form of a linear equation is one of the most straightforward forms to work with when graphing a line. This form of the equation is written as \(y = mx + b\). Here, \(m\) represents the slope of the line, while \(b\) indicates the y-intercept.
  • Having an equation in this form allows you to quickly identify critical components for graphing.
  • First, it shows the slope, which determines the line's angle and direction.
  • Second, it reveals the y-intercept, or where the line crosses the y-axis.
By rearranging an equation to fit the slope-intercept form, graphing becomes a much simpler task. You can plot the y-intercept first and use the slope to determine the path of the line across the graph.
Y-Intercept
The y-intercept is a crucial part of understanding and graphing linear equations. It represents the point where the line intersects the y-axis. In the slope-intercept form \(y = mx + b\), the y-intercept is the constant term \(b\).
  • The value of \(b\) shows where the line will meet the y-axis. For instance, if the y-intercept \(b\) = 4, the line will cross the y-axis at the point (0,4).
  • This point is your starting spot for graphing the line. From there, you can use the slope to determine the rest of the line.
Remember, the y-intercept is always located on the y-axis, and it鈥檚 invaluable for quickly drawing and understanding the graph of a linear equation.
Slope of a Line
The slope of a line is an essential concept to grasp when dealing with linear equations. Simply put, it measures the steepness or incline of the line. In the slope-intercept form \(y = mx + b\), the slope \(m\) indicates how much the y-value of a point on the line changes as the x-value increases by one unit.
  • For example, a slope of 3 means that for every step you take to the right along the x-axis, the line moves up 3 units.
  • The slope can be both positive or negative, with positive slopes slanting upwards and negative ones slanting downwards.
A quick way to remember the slope concept is "rise over run," where the rise refers to the change in vertical direction, and run is the change in the horizontal direction. Understanding slope is critical for not only graphing lines but also for predicting their direction and steepness on a graph.

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

Express each combined variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 4. (OBJECTIVE 4) \(y\) varies directly with \(a\) and inversely with \(b .\) If \(y=3\) when \(a=4\) and \(b=12,\) find \(y\) when \(a=10\) and \(b=18\).

Graph each equation using any method. $$y=4.5 x+2$$

Set up a variation equation and solve for the requested value. Assume that the value of a machine varies inversely with its age. If a drill press is worth \(300\)dollar when it is 2 years old, find its value when it is 6 years old. How much has the machine depreciated in those 4 years?

Express each direct variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 1. (OBJECTIVE 1) \(d\) varies directly with \(t .\) If \(d=15\) when \(t=3,\) find \(t\) when \(d=3\).

Graph each equation using any method. $$x=0$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.