/*! 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 equation. Solve for \(y\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 61

Graph equation. Solve for \(y\) first, when necessary. \(y=1.5 x-4\)

Short Answer

Expert verified
Graph the line with y-intercept at (0, -4) and slope of 1.5, passing through (2, -1).

Step by step solution

01

Identify the Equation Format

The equation given is in the slope-intercept form, which is written as \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
02

Identify the Slope

In the equation \(y = 1.5x - 4\), the slope \(m\) is 1.5.
03

Identify the Y-intercept

In the equation \(y = 1.5x - 4\), the y-intercept \(b\) is -4. This tells us that the line crosses the y-axis at (0, -4).
04

Plot the Y-intercept

Start by plotting the y-intercept at the point (0, -4) on the graph. This is where the line will start.
05

Use the Slope to Find Another Point

The slope is 1.5, which can be written as a fraction \(\frac{3}{2}\). This means that for every 2 units you move to the right, you move up 3 units. Starting from the y-intercept (0, -4), move 2 units to the right, and then 3 units up to locate the next point (2, -1).
06

Draw the Line

After plotting the points (0, -4) and (2, -1), draw a straight line through these points to extend across the graph.

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 fundamental ways to express a line. It's written as \( y = mx + b \), where \( m \) represents the slope of the line, and \( b \) represents the y-intercept. This form is extremely useful because it instantly reveals both the direction and the starting point of the line on a graph.
  • The slope \( m \) indicates how steep the line is. If \( m \) is positive, the line slopes upward as you move from left to right. If negative, the line slopes downward.
  • The y-intercept \( b \) is the point where the line crosses the y-axis. This point allows you to begin plotting the graph of the equation.
Understanding this form makes it easy to quickly sketch graphs and analyze linear equations.
Graphing Linear Equations
Graphing linear equations is a straightforward process once you understand the equation's format. The goal is to represent the equation visually on a coordinate plane. Begin with the y-intercept, which serves as your anchor point on the graph. From there, use the slope to determine the direction and steepness of the line.
  • Start by plotting the y-intercept \( (0, b) \), where \( b \) is the value from the slope-intercept form.
  • Utilize the slope to find additional points. The slope \( \frac{rise}{run} \) tells you how to move from one point to another. Rise refers to the change in the vertical direction, and run refers to the change in the horizontal direction.
  • Join these points with a straight line, extending across the graph.
This visual representation helps in understanding the behavior of the line as \( x \) changes.
Slope and Y-Intercept
The slope and y-intercept are crucial components in describing linear relationships. They provide a complete picture of how a line behaves and its position on a graph.
  • Slope (\( m \)): The slope determines the angle of the line's incline. A steep slope (large value) indicates a more pronounced tilt, whereas a gentle slope (small value) indicates a flatter line. The slope can be expressed as a fraction \( \frac{rise}{run} \), showing the vertical change per unit of horizontal shift.
  • Y-intercept (\( b \)): The y-intercept is where the line crosses the y-axis, providing a starting point for graphing the line. It signifies the value of \( y \) when \( x \) is zero.
By understanding both elements, you can accurately plot any linear equation and predict how changes in \( x \) will affect \( y \). These concepts play a crucial role not only in graphing but also in analyzing real-world situations where linear relationships are involved.

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

Production Costs. A television production company charges a basic fee of \(\$ 5,000\) and then \(\$ 2,000\) an hour when filming a commercial. a. Write a linear equation that describes the relationship between the total production costs \(c\) and the hours \(h\) of filming. b. Use your answer to part a to find the production costs if a commercial required 8 hours of filming

Find the slope of a line perpendicular to the line passing through the given two points. See Example \(9 .\) \(\left(-2, \frac{1}{2}\right)\) and \(\left(-1, \frac{3}{2}\right)\)

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6 $$ \begin{aligned} &-2 y=2-x\\\ &2 x-3=4 y \end{aligned} $$

Explain how to decide which side of the boundary line to shade when graphing a linear inequality in two variables.

A sporting goods manufacturer allocates at least \(2,400\) units of production time per day to make baseballs and footballs. It takes 20 units of time to make a baseball and 30 units of time to make a football. If \(x\) represents the number of baseballs made and \(y\) represents the number of footballs made, the graph of \(20 x+30 y \geq 2,400\) shows the possible ways to schedule the production time. Graph the inequality. Then find three possible combinations of production time for the company to make baseballs and footballs.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

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.