/*! 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 20 In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 20

In the following exercises, graph by plotting points. $$ y=\frac{3}{2} x-3 $$

Short Answer

Expert verified
Plot points: \((-2, -6)\), \((0, -3)\), \((2, 0)\), \((4, 3)\). Connect points with a line.

Step by step solution

01

Create a Table of Values

Choose several values for \( x \), and use the equation \( y = \frac{3}{2}x - 3 \) to find the corresponding \( y \) values. For example, choose \( x = -2, 0, 2, 4 \).
02

Calculate \( y \) Values

Substitute each chosen \( x \) value into the equation to find the corresponding \( y \) values: For \( x = -2 \), \( y = \frac{3}{2}(-2) - 3 = -3 - 3 = -6 \). For \( x = 0 \), \( y = \frac{3}{2}(0) - 3 = 0 - 3 = -3 \). For \( x = 2 \), \( y = \frac{3}{2}(2) - 3 = 3 - 3 = 0 \). For \( x = 4 \), \( y = \frac{3}{2}(4) - 3 = 6 - 3 = 3 \).
03

List the Points

Based on the calculations, the points to be plotted are \((-2, -6)\), \((0, -3)\), \((2, 0)\), and \((4, 3)\).
04

Plot the Points on a Graph

Draw a Cartesian coordinate system. Plot the points \((-2, -6)\), \((0, -3)\), \((2, 0)\), and \((4, 3)\).
05

Draw the Line

Connect the plotted points with a straight line to complete the graph of the equation \( y = \frac{3}{2}x - 3 \).

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.

Plotting Points
Plotting points is essential in graphing equations. It involves placing dots on a graph to represent solutions. Each point has an x-value (horizontal) and a y-value (vertical).

To plot a point, start at the origin (0,0). Move right if the x-value is positive, or left if it's negative. Then, move up if the y-value is positive, or down if it's negative.

For instance, for the point (-2, -6), you start at the origin, move two steps left, and six steps down to place your point.
Cartesian Coordinate System
The Cartesian Coordinate System is a two-dimensional plane with a horizontal x-axis and a vertical y-axis.

It divides the plane into four quadrants. Points are written as (x, y) and show the position relative to these axes.

For graphing equations, draw a graph paper, mark units along both axes, and label them to ensure clarity. Plot the points correctly as described, ensuring the axes are evenly spaced and the plotted points are accurate.
Linear Functions
A linear function is an equation of a straight line. It usually takes the form y = mx + b, where m is the slope and b is the y-intercept.

Linear functions have constant rates of change, meaning their graphs show a straight line. This indicates a consistent relationship between x and y values.

For example, y = (3/2)x - 3 is a linear function. It shows how y changes with x at a constant rate of 3/2. Graphing several x-values helps visualize this straight-line relationship.
Slope and Y-Intercept
The slope and y-intercept are key features of linear functions. The slope (m) measures the steepness of the line, calculated as the rise over the run (change in y over change in x).

The y-intercept (b) is where the line crosses the y-axis. It shows the value of y when x is zero.

In the equation y = (3/2)x - 3, the slope is 3/2, meaning for every 2 units you move right, you go up 3 units. The y-intercept is -3, meaning the line crosses the y-axis at -3. To draw the line, plot the y-intercept first, then use the slope to find other points.

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, use the set of ordered pairs to ( ) determine whether the relation is a function, (b) find the domain of the relation, and \(\odot\) find the range of the relation. . \(\\{(9,-3),(4,-2),(1,-1),\) (0,0),(1,1),(4,2),(9,3)\\}

In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. $$ f(x)=|x|+1 $$

The daily cost to the printing company to print a book is modeled by the function \(C(x)=3.25 x+1500\) where \(C\) is the total daily cost and \(x\) is the number of books printed. (a) Determine the independent and dependent variable. (b) Find \(C(0)\). Explain what this result means. (c) Find \(C(1000)\). Explain what this result means.

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

In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. $$ f(x)=|x|-1 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.