/*! 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 39 Find the slope of the line satis... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 39

Find the slope of the line satisfying the given conditions. through \((5,9)\) and \((-2,9)\)

Short Answer

Expert verified
The slope is 0.

Step by step solution

01

Identify the formula

The formula for the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[m = \frac{y_2 - y_1}{x_2 - x_1}\]
02

Substitute the points into the formula

The given points are \((5,9)\) and \((-2,9)\). Substitute \(x_1 = 5\), \(y_1 = 9\), \(x_2 = -2\), and \(y_2 = 9\) into the formula: \[m = \frac{9 - 9}{-2 - 5}\]
03

Simplify the numerator

Calculate the difference in the y-coordinates: \[y_2 - y_1 = 9 - 9 = 0\]
04

Simplify the denominator

Calculate the difference in the x-coordinates: \[-2 - 5 = -7\]
05

Calculate the slope

Substitute the simplified numerator and denominator back into the formula: \[m = \frac{0}{-7} = 0\]

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 formula
The slope of a line represents how steep the line is. It is a measure of the change in the vertical direction (up or down) for each unit of change in the horizontal direction (left or right). To find the slope between two points, we use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] . In this formula, \( m \) represents the slope, \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points. By substituting the coordinates into this formula and simplifying, we get the slope. This formula helps in understanding how the line changes between any two given points.
coordinate geometry
Coordinate geometry, also known as analytic geometry, is a branch of geometry that uses a coordinate system to study the relationships between points, lines, and other geometric shapes. We use coordinates like \( (x, y) \) to represent points in a plane. For our problem, the points are \( (5, 9) \) and \( (-2, 9) \). By plotting these points on a graph, you can see they lie on a horizontal line. When two points have the same y-coordinate, the line passing through them will always be horizontal. The slope of a horizontal line, as seen in this problem, is always zero.
simplifying fractions
Simplifying fractions is an important step in solving many mathematical problems. It involves reducing a fraction to its simplest form where the numerator and the denominator have no common factors other than 1. In our problem, after substituting the coordinates into the slope formula, we get \[ m = \frac{9-9}{-2-5} \] . Simplifying the numerator: \ 9 - 9 = 0 \, and simplifying the denominator: \ -2 - 5 = -7 \, we get the fraction \ \frac{0}{-7} \. Since any number divided by zero is zero, the slope simplifies to \ m = 0 \. This means the simplified fraction directly shows the slope of the line.

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

Solve each problem. To visualize the situation, use graph paper and a pair of compasses to carefully draw the graphs of the circles. Suppose that receiving stations \(X, Y,\) and \(Z\) are located on a coordinate plane at the points \((7,4),(-9,-4),\) and \((-3,9),\) respectively. The epicenter of an earthquake is determined to be 5 units from \(X, 13\) units from \(Y\), and 10 units from \(Z\). Where on the coordinate plane is the epicenter located?

Determine whether the three points are collinear by using slopes. $$(0,9),(-3,-7),(2,19)$$

Give the slope and y-intercept of each line, and graph it. $$y-\frac{3}{2} x-1=0$$

Give the slope and y-intercept of each line, and graph it. $$4 x-y=7$$

Solve each problem. cost of Private College Education The table lists the average annual cost (in dollars) of tuition and fees at private four-year colleges for selected years. (a) Determine a linear function \(f(x)=m x+b\) that models the data, where \(x=0\) represents 1996 \(x=1\) represents \(1997,\) and so on. Use the points \((0,12,881)\) and \((12,22,449)\) to graph \(f\) and a scatter diagram of the data on the same coordinate axes. (You may wish to use a graphing calculator.) What does the slope of the graph of \(f\) indicate? (b) Use this function to approximate tuition and fees in \(2007 .\) Compare your approximation to the actual value of \(\$ 21,979\). (c) Use the linear regression feature of a graphing calculator to find the equation of the line of best fit.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

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.