/*! 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 98 In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 98

In the following exercises, graph each equation. $$ y=2 x $$

Short Answer

Expert verified
Graph points:(-2, -4), (0, 0), (2, 4).Then draw the line.

Step by step solution

01

- Understand the Equation

The given equation is in the form of a linear equation, represented as y = mx, where m is the slope of the line. For the equation y = 2x, the slope (m) is 2.
02

- Find Key Points

Select a few values for x to determine the corresponding values of y. For example, if x = -2, then y = 2(-2) = -4. If x = 0, then y = 2(0) = 0. If x = 2, then y = 2(2) = 4.
03

- Plot the Points

Plot the points on a coordinate plane: (-2, -4), (0, 0), and (2, 4).
04

- Draw the Line

Draw a straight line through the plotted points. This line represents the equation y = 2x.

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
Linear equations are equations where the highest power of the variable is 1. They take the general form of y = mx + b.
In this form, 'm' is the slope and 'b' is the y-intercept.
When graphing, the slope \(m\) tells you how the line rises or falls, and the y-intercept \(b\) tells you where the line crosses the y-axis.
In the given example, \(y = 2x\), we can see that 'm' is 2 and 'b' is 0, making it a line that passes through the origin (0,0) and has a slope of 2.
slope
The slope of a line measures its steepness and direction. It is calculated as the ratio of the rise (the change in the y-coordinates) to the run (the change in the x-coordinates).
Mathematically, it is represented as \(\frac{y_2 - y_1}{x_2 - x_1}\).
For the equation \(y = 2x\), the slope is 2. This means for every 1 unit increase in 'x', 'y' increases by 2 units.
Understanding slope is essential because it not only tells us how steep the line is but also the direction it moves. A positive slope means the line rises as it moves to the right, while a negative slope means the line falls.
coordinate plane
The coordinate plane is a two-dimensional surface where we can plot points, lines, and curves using an x-axis (horizontal) and a y-axis (vertical).
Each point on the coordinate plane is represented by an ordered pair \( (x, y) \).
When graphing a linear equation like \( y = 2x \), we use the coordinate plane to plot key points and draw the line through them.
The point where the x-axis and y-axis intersect is called the origin, represented by (0,0).
Plotting is easier when you understand this fundamental layout, as it helps you locate points accurately.
plotting points
Plotting points involves marking specific coordinates on the coordinate plane.
For the equation \( y = 2x \), we select values for 'x' and use the equation to find the corresponding 'y' values.
For example, if x = -2, then y = 2(-2) = -4, giving us the point (-2, -4).
Similarly, we can choose x = 0 to get the point (0, 0), and x = 2 to get the point (2, 4).
Plot these points on the coordinate plane, and draw a straight line through them to visualize the linear equation.
Accurate plotting is crucial for creating a correct graph and understanding the relationship between variables.

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, graph each equation. $$ y=5 $$

In the following exercises, graph each pair of equations in the same rectangular coordinate system. $$ y=5 x \text { and } y=5 $$

In the following exercises, find three solutions to each linear equation. $$ y=-x-1 $$

Find the slope of the line \(y=2 .\)

In the following exercises, plot each point in a rectangular coordinate system. $$(1,3),(3,1)$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Decision Maths

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.