/*! 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 25 Graph each function. $$f(x)=2 ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 25

Graph each function. $$f(x)=2 x-5$$

Short Answer

Expert verified
Graph the line passing through (0, -5) and (1, -3).

Step by step solution

01

Identify the Type of Function

The function given is a linear function because it has the form of a linear equation, which is generally written as \[f(x) = mx + b\]Here, \[m = 2\] and \[b = -5\].
02

Determine the Slope and Y-Intercept

From the function \[f(x) = 2x - 5\], the slope (\[m\]) is \[2\], and the Y-intercept (\[b\]) is \[-5\].The Y-intercept is the point where the graph crosses the Y-axis, which is \[(0, -5)\].
03

Plot the Y-Intercept

Start by plotting the Y-intercept \[(0, -5)\] on the graph.
04

Use the Slope to Determine Another Point

Using the slope \[m = 2\], which means \[ \text{rise } = 2 \text{ and run } = 1\], start at the Y-intercept \[(0, -5)\] and move up 2 units and 1 unit to the right to find the next point \[(1, -3)\].
05

Plot the Second Point

Plot the second point \[(1, -3)\] on the graph.
06

Draw the Line

Draw a straight line through the points \[(0, -5)\] and \[(1, -3)\]. This line is the graph of the function \[f(x) = 2x - 5\].

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
In mathematics, the slope of a line is a measure of its steepness and direction. It's denoted by the letter italic{m}. The slope can be viewed as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. In the function italic{f(x) = 2x - 5}, the slope is italic{2}. This means for every 1 unit you move to the right on the x-axis, you move 2 units up on the y-axis.
  • A positive slope means the line is going upwards as you move to the right.
  • A negative slope means the line is going downwards as you move to the right.
  • A slope of zero means the line is horizontal.
You can find the slope by using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]Where (x_1, y_1) and (x_2, y_2) are any two points on the line.
y-intercept
The Y-intercept of a line is the point where the line crosses the y-axis. It's represented by the letter italic{b}in the linear equation italic{f(x) = mx + b}. In our given function italic{f(x) = 2x - 5}, the Y-intercept is italic{-5}.
To find the Y-intercept:
  • Set italic{x} to 0 in the equation.
  • Solve for italic{f(x)} (which is the same as italic{y}).
For italic{f(x) = 2x - 5}, when italic{x} = 0, f(0) = -5, so the Y-intercept is (0, -5). This point helps in starting the graph of the linear function, as it's always on the y-axis.
linear equation
A linear equation produces a straight line when graphed. The standard form of a linear equation is italic{f(x) = mx + b}. Here, italic{m} is the slope and italic{b} is the Y-intercept. For the function italic{f(x) = 2x - 5}, we recognize it is linear because it fits this form.

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

Find the domain of each function given below. $$g(x)=x^{2}-2 x+1$$

Find the equilibrium point for the following demand and supply functions, where \(q\) is the quantity, in thousands of units, and \(x\) is the price per unit, in dollars. Demand: \(q=83-x\) Supply: \(\quad q=\frac{x^{2}}{576}-1.9\)

Determine the domain of each function. $$f(x)=\sqrt[4]{7-x}$$

Find the domain of each function given below. $$f(x)=x^{2}+3$$

Find the domain of each function given below. \(g(x)=\frac{3 x-10}{x^{2}-4 x-5} \quad\) (Hint: Factor the denominator.)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

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.