/*! 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 26 Graph equation by hand. \(y=-3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 26

Graph equation by hand. \(y=-3 x\)

Short Answer

Expert verified
Graph passes through (0,0) and (1,-3) with slope -3.

Step by step solution

01

- Identify the Equation Type

The given equation is a linear equation of the form: \(y = mx + b\). Here, \(m = -3\) and \(b = 0\), making it a line that passes through the origin.
02

- Determine the Slope

The slope \(m\) is \(-3\). This means that for every unit increase in \(x\), \(y\) decreases by 3 units.
03

- Find Initial Point

Since \(b = 0\), the line passes through the origin (0, 0). This is our initial point.
04

- Plot the Initial Point

On a graph, plot the initial point (0, 0).
05

- Use the Slope to Find Another Point

Starting at the origin (0, 0), use the slope \(-3\). For instance, if \(x = 1\), then \(y = -3(1) = -3\). Plot the point (1, -3).
06

- Draw the Line

Draw a straight line passing through the points (0, 0) and (1, -3). Ensure the line extends in both directions to indicate it goes to infinity.
07

- Label the Axes

Label the x-axis and y-axis and add arrows to indicate their direction.

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 Slope-Intercept Form
The slope-intercept form of a linear equation is very useful for graphing. It is written as \[ y = mx + b \], where
  • m is the slope of the line
  • b is the y-intercept, where the line crosses the y-axis
For example, in the equation \( y = -3x \), the slope (m) is -3. This means the line falls 3 units for every 1 unit it moves to the right. Since b (the y-intercept) is 0, this means it passes through the origin (0,0).
Plotting Points on a Graph
To graph any linear equation, we need at least two points. Here鈥檚 how:
  • Start by plotting the y-intercept (the point where the line crosses the y-axis). For \( y = -3x \), this is (0, 0).
  • Use the slope to find another point. The slope of -3 means that for every increase of 1 in x, y decreases by 3. So, you can find another point by moving 1 unit to the right (increasing x by 1) and 3 units down (decreasing y by 3).
We get the point (1, -3). Plot this on your graph. Once you have the points (0,0) and (1,-3), you can draw the line through them extending in both directions.
Basics of Linear Equations
Linear equations represent straight lines on a graph. They have a constant rate of change, which means they have a constant slope. Consider the general form of a linear equation: \[ y = mx + b \]
  • The term m tells us how steep the line is. A positive slope means the line rises as you move to the right, while a negative slope means it falls.
  • The term b shows where the line crosses the y-axis.
For our equation, \( y = -3x \), the line has a steep negative slope and crosses the y-axis at (0,0). This constant rate of change is what defines linear relationships.

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

In 2003 , Americans recovered 72.3 million tons of solid waste. In 2007 , the figure grew to 85.0 million tons. Let \(N\) represent the number of tons recovered, in millions, and \(t\) the number of years since \(2000 .\) Source: U.S. Environmental Protection Agency a) Find a linear equation that fits the data. b) Predict the amount recycled in 2010 .

To prepare for Section \(3.8,\) review evaluating algebraic expressions (Section \(1.8)\) $$ 3-4 x, \text { for } x=5 $$

Records in the 400-m Rum. The record \(R(t)\) for the \(400-\mathrm{m}\) run \(t\) years after 1930 is given by \(R(t)=\) \(46.8-0.075 t\). a) What do the numbers 46.8 and \(-0.075\) signify? b) When will the record be 38.7 sec? c) What is the domain of \(R ?\)

If \(f(x)=4-x,\) for what input is the output 7?

Write a slope-intercept equation of the line whose graph is described. Perpendicular to the graph of \(2 x+y=0\) \(y\) -intercept \((0,0)\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and 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.