/*! 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 4 Find the slope of the line that ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 4

Find the slope of the line that contains the points (2,11) and (6,-5) .

Short Answer

Expert verified
The slope of the line containing the points (2,11) and (6,-5) is -4.

Step by step solution

01

Identify the coordinates of the given points.

We are given two points: (2,11) and (6,-5). We can identify: \(x_1 = 2\), \(y_1 = 11\), \(x_2 = 6\), and \(y_2 = -5\).
02

Use the slope formula to find the slope.

Now we can plug the coordinates of the points into the slope formula: $$m = \frac{y2 - y1}{x2 - x1}$$ $$m = \frac{(-5) - 11}{6 - 2}$$
03

Calculate the slope.

Now we can calculate the slope: $$m = \frac{(-5) - 11}{6 - 2} = \frac{-16}{4}$$ $$m = -4$$ The slope of the line containing the points (2,11) and (6,-5) is -4.

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.

Coordinate Geometry
When dealing with lines on a plane, we often refer to the Cartesian coordinate system, which precisely allows us to locate points and analyze geometric properties like lines and shapes. In the context of our exercise, coordinate geometry helps us perform computations over the plane by considering the positions of points like (2, 11) and (6, -5).

Some key elements of coordinate geometry include:
  • A two-dimensional plane defined by the x-axis and y-axis.
  • The capability to pinpoint locations on this plane using coordinates (x, y).
  • The implementation of formulas to find distances, slopes, and angles between points or lines.
By using the coordinates provided, coordinate geometry allows us to engage in computations, like finding the slope of a line, that help us better understand spatial relationships between points.
Linear Equation
Linear equations describe lines on a coordinate plane and are central to analyzing geometric elements like lines. In simple terms, a linear equation is an equation that models a straight line. It typically appears in the form: \[ y = mx + b \]where:
  • \( y \) is the dependent variable.
  • \( m \) represents the slope of the line.
  • \( x \) is the independent variable.
  • \( b \) is the y-intercept, which is the value of \( y \) when \( x \) is 0.
In the context of our exercise, knowing the slope of the line assists in forming this type of equation. The slope and y-intercept are vital for constructing the linear equation when both are determined, fully describing the line in the coordinate plane.
Slope Formula
The Slope Formula is a fundamental concept in coordinate geometry as it provides a way to calculate the steepness or incline of a line. This calculation is crucial in determining how two points relate to one another on a plane.

The slope formula, often represented as:\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]is used to find the slope (\( m \)) of a line passing through two points: \((x_1, y_1)\) and \((x_2, y_2)\).

Here is how it works:
  • The formula calculates the vertical change (\( y_2 - y_1 \)) and divides it by the horizontal change (\( x_2 - x_1 \)) between two points.
  • This ratio reflects how steep the line is, which can be positive (rising line), negative (falling line), zero (horizontal), or even undefined (vertical).
In our example, the calculated slope of -4 indicates that for every unit we move horizontally to the right, the line drops 4 units downwards, highlighting a steep decline.

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

Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ (s(x))^{2} t(x) $$

Write the domain of the given function \(r\) as a union of intervals. $$ r(x)=\frac{4 x^{7}+8 x^{2}-1}{x^{2}-2 x-6} $$

Find the asymptotes of the graph of the given function \(\mathrm{r}\). $$ r(x)=\frac{9 x+5}{x^{2}-x-6} $$

Without doing any calculations or using a calculator, explain why $$ x^{2}+87559743 x-787727821 $$ has no integer zeros. [Hint: If \(x\) is an odd integer, is the expression above even or odd? If \(x\) is an even integer, is the expression above even or odd?]

Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ (t \circ r)(x) $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.