/*! 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 21 In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 21

In the following exercises, graph by plotting points. $$ y=-\frac{2}{5} x+1 $$

Short Answer

Expert verified
Plot points (0, 1) and (5, -1), then draw the line through them.

Step by step solution

01

- Identify the slope and y-intercept

The equation of the line is given in slope-intercept form, which is \( y = mx + b \). Here, \( m = -\frac{2}{5} \) (the slope) and \( b = 1 \) (the y-intercept).
02

- Plot the y-intercept

To plot the y-intercept, find the point where the line crosses the y-axis. Because \( b = 1 \), plot the point \( (0, 1) \) on the graph.
03

- Determine another point using the slope

The slope \( m = -\frac{2}{5} \) means that for every 5 units horizontally to the right, the line moves 2 units down. Starting from the y-intercept point \( (0, 1) \), move 5 units to the right (to \( x = 5 \)) and 2 units down (to \( y = -1 \)). Plot the point \( (5, -1) \).
04

- Draw the line

With the points \( (0, 1) \) and \( (5, -1) \) plotted, use a ruler to draw a straight line through these points. This line represents the equation \( y = -\frac{2}{5} x + 1 \).

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 common ways to express a linear equation. It is represented as \( y = mx + b \), where:

  • \( m \) is the slope of the line

  • \( b \) is the y-intercept


Understanding this form helps you easily find the slope and y-intercept directly from the equation.
In the given exercise, the equation is \( y = -\frac{2}{5} x + 1 \).
Here, the slope \( m = -\frac{2}{5} \) and the \( b \) value or y-intercept is 1. These values are essential for graphing the equation accurately.
Plotting Points
Plotting points is a classic method to graph a linear equation. Start by identifying critical points from the equation, such as the y-intercept and any additional points derived from the slope.
The steps are as follows:

  • First, plot the y-intercept. For \( y = -\frac{2}{5} x + 1 \), this point is \( (0, 1) \).

  • Next, find another point using the slope. The slope defines the rise over the run. For \( m = -\frac{2}{5} \), it means for every 5 units you move to the right, move 2 units down. From \( (0, 1) \), moving right 5 units to \( x = 5 \) and down 2 units to \( y = -1 \) gives the point \( (5, -1) \).

  • Finally, plot these points and draw a straight line through them. This line represents the given linear equation.


Plotting these points correctly ensures an accurate graph of the linear equation.
Slope and Y-Intercept
The slope and y-intercept are fundamental concepts in graphing linear equations.

  • The slope \( m \) indicates how steep the line is and its direction (upward or downward). In the equation \( y = -\frac{2}{5} x + 1 \), the slope \( -\frac{2}{5} \) shows the line goes downwards as you move from left to right.

  • The y-intercept \( b \) is the point where the line crosses the y-axis. For \( b = 1 \), the y-intercept is \( (0, 1) \). This is your starting point when plotting your graph.


Together, these values help determine the exact placement and incline of your line on a graph. Always start with the y-intercept and use the slope to find other points along the line.

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 the following exercises, evaluate the function: (@) \(f(2)\) (b) \(f(-1)\) (c) \(f(a) .\) $$ f(x)=-4 x+2 $$

In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. $$ f(x)=3 x $$

In the following exercises, evaluate the function. \(g(x)=\frac{x-2}{x+2} ; g(4)\)

Graph the linear inequality: \(x-y \leq 3\)

In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. $$ f(x)=2 \sqrt{x} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics 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.