/*! 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 79 Graph equation. Solve for \(y\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 79

Graph equation. Solve for \(y\) first, when necessary. \(y=-2.5 x+5\)

Short Answer

Expert verified
Graph by plotting the points (0,5) and (2,0), then draw a line through them.

Step by step solution

01

Identifying the Equation

We are given the linear equation in the slope-intercept form: \(y = -2.5x + 5\) where \(y\) is already isolated. Therefore, there is no need to solve for \(y\) because it's already solved.
02

Understanding the Slope and Y-Intercept

The equation \(y = -2.5x + 5\) is in the slope-intercept form \(y = mx + b\). Here, \(m = -2.5\) represents the slope, and \(b = 5\) is the y-intercept. This means the graph will cross the y-axis at \(5\).
03

Plotting the Y-Intercept

Start by plotting the y-intercept on the graph. Since \(b = 5\), place a point on the y-axis at \( (0, 5) \).
04

Using the Slope to Plot the Next Point

The slope \(-2.5\) can be expressed as \(-\frac{5}{2}\), meaning a change of -5 units in the y-direction for a change of 2 units in the x-direction. From the point \((0,5)\), move 2 units to the right (positive x-direction) to \((2,?)\), then move 5 units down (negative y-direction) to \((2,0)\). Plot this second point at \((2,0)\).
05

Drawing the Line

Draw a straight line through the points \((0, 5)\) and \((2, 0)\). This is the graph of the equation \(y = -2.5x + 5\).

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 a powerful tool used in graphing linear equations. It's expressed as \( y = mx + b \), where "\(m\)" represents the slope and "\(b\)" is the y-intercept. This form is super convenient because it straightforwardly gives us the core details needed to graph a line: the slope and where the line intersects the y-axis.
  • "\( m \)" tells us how steep the line is and its direction (whether it goes up or down).
  • "\( b \)" helps us know exactly where to start drawing our line on the graph.
Understanding this structure allows you to sketch graphs quickly without complicated calculations. Whether your slope is a fraction, a whole number, or negative, the slope-intercept form makes it clear and easy to interpret.
Y-Intercept
The y-intercept is the point where the line crosses the y-axis. In the equation \( y = mx + b \), it's represented by "\(b\)". This value is essential because it gives you the starting point for graphing your line. Let's break it down:- Since the y-axis runs vertically, the x-coordinate of this point is always zero.- For the equation \( y = -2.5x + 5 \), the y-intercept is at \((0, 5)\).This means you already have one reliable point on your graph. If you imagine the line, it starts touching the y-axis precisely at \((0, 5)\). It may seem like a small detail, but it's a fundamental piece that simplifies constructing the rest of your graph.
Plotting Points
Plotting points on a graph involves marking certain coordinates that the linear equation will pass through. To begin, use your y-intercept. You can then apply the slope to determine additional points.
  • Start with the y-intercept point, given as \((0, b)\).
  • For the equation \( y = -2.5x + 5 \), this is the point \((0, 5)\).
Next, utilize the slope to find another point:- If the slope is expressed as a fraction, such as \(-\frac{5}{2}\), start from your y-intercept.- Then, move horizontally based on the denominator (2 to the right), and vertically with the numerator (-5 down).- Mark the new point based on these directions.Plot these points to visually represent the equation, providing a clear visual of how the line behaves.
Slope Calculation
The slope of a line indicates the direction and steepness. It's determined from the equation in slope-intercept form by the coefficient "\(m\)". In the example \( y = -2.5x + 5 \):- The slope "\(m\)" is \(-2.5\). Slope can be rewritten as a fraction to show steps between points. For instance:- \(-2.5\) can be \(-\frac{5}{2}\) 鈥� meaning for every 2 units moved right, you descend 5 units.This allows precise movement between points on the graph:
  • Start with your known point, like the y-intercept \((0, 5)\).
  • From there, use the slope to move to your next point, which in this equation brings you to \((2, 0)\).
Using the slope accurately, you ensure your graph reflects the equation's true nature. Keep in mind, a negative slope like this one creates a descending line, moving downwards as it progresses.

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

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6 $$ \begin{aligned} &3 x=5 y-10\\\ &5 x=1-3 y \end{aligned} $$

Streets. One of the steepest streets in the United States is Eldred Street in Highland Park, California (near Los Angeles). It rises approximately 220 feet over a horizontal distance of 665 feet. What is the grade of the street? (IMAGE CANNOT COPY)

Subscripts are used in other disciplines besides mathematics. In what disciplines are the following symbols used? a. \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CO}_{2}\) b. \(\mathrm{C}_{7}\) and \(\mathrm{G}_{7}\) c. \(\mathrm{B}_{6}\) and \(\mathrm{B}_{12}\)

If the graph of \(y=m x+b\) passes through quadrants I, II, and IV, what can be known about the constants \(m\) and \(b ?\)

Find an equation of the line that passes through \((2,5)\) and is parallel to the line \(y=4 x-7 .\) Write the equation in slope-intercept form.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.