/*! 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 14 Graph of a linear function Find ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 14

Graph of a linear function Find and graph the linear function that passes through the points (2,-3) and (5,0)

Short Answer

Expert verified
Answer: The equation of the line passing through the points (2, -3) and (5, 0) is y = 1x - 5. Its graph is a straight line going through the points (2, -3) and (5, 0).

Step by step solution

01

Find the slope (m)

Use the slope formula: m = (y2 - y1) / (x2 - x1) Let (x1, y1) = (2, -3) and (x2, y2) = (5, 0) m = (0 - (-3)) / (5 - 2) m = 3/3 m = 1
02

Substitute the slope (m) and one of the points (x, y) into the equation y = mx + b

Let's use the point (2, -3) -3 = 1 * 2 + b
03

Solve for b

We have -3 = 1 * 2 + b b = -3 - 2 b = -5
04

Write the linear equation using the values of m and b

We know that m = 1 and b = -5. Plugging these values into the equation y = mx + b, we have y = 1x - 5
05

Graph the linear function y = 1x - 5

To graph the function, we'll need to plot at least two points. Since we are given two points already, (2, -3) and (5, 0), we don't need to find any more points. Plot the points (2, -3) and (5, 0) on the graph and draw a straight line passing through those points. The graph of the linear function y = 1x - 5 will be a straight line going through these points.

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!

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

Sketch a graph of the given pair of functions to conjecture a relationship between the two functions. Then verify the conjecture. $$\tan ^{-1} x ; \frac{\pi}{2}-\cot ^{-1} x$$

The height of a baseball hit straight up from the ground with an initial velocity of \(64 \mathrm{ft} / \mathrm{s}\) is given by \(h=f(t)=\) \(64 t-16 t^{2},\) where \(t\) is measured in seconds after the hit. a. Is this function one-to-one on the interval \(0 \leq t \leq 4 ?\) b. Find the inverse function that gives the time \(t\) at which the ball is at height \(h\) as the ball travels upward. Express your answer in the form \(t=f^{-1}(h)\). c. Find the inverse function that gives the time \(t\) at which the ball is at height \(h\) as the ball travels downward. Express your answer in the form \(t=f^{-1}(h)\). d. At what time is the ball at a height of \(30 \mathrm{ft}\) on the way up? e. At what time is the ball at a height of \(10 \mathrm{ft}\) on the way down?

a. Let \(g(x)=2 x+3\) and \(h(x)=x^{3} .\) Consider the composite function \(f(x)=g(h(x))\). Find \(f^{-1}\) directly and then express it in terms of \(g^{-1}\) and \(h^{-1}\). b. Let \(g(x)=x^{2}+1\) and \(h(x)=\sqrt{x} .\) Consider the composite function \(f(x)=g(h(x))\). Find \(f^{-1}\) directly and then express it in terms of \(g^{-1}\) and \(h^{-1}\). c. Explain why if \(g\) and \(h\) are one-to-one, the inverse of \(f(x)=g(h(x))\) exists.

Beginning with the graphs of \(y=\sin x\) or \(y=\cos x,\) use shifting and scaling transformations to sketch the graph of the following functions. Use a graphing utility only to check your work. $$q(x)=3.6 \cos (\pi x / 24)+2$$

The Earth is approximately circular in cross section, with a circumference at the equator of 24,882 miles. Suppose we use two ropes to create two concentric circles; one by wrapping a rope around the equator and then a second circle that is \(38 \mathrm{ft}\) longer than the first rope (see figure). How much space is between the ropes?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

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.