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

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 14

Find the slope of the line that passes through each pair of points. $$ (-8,-3),(2,3) $$

Short Answer

Expert verified
The slope is \(\frac{3}{5}\).

Step by step solution

01

Recall the Slope Formula

The slope of a line passing through two points \(x_1, y_1\) and \(x_2, y_2\) is given by the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). This formula calculates the change in \(y\) divided by the change in \(x\).
02

Identify the Coordinates

Here, the two points given are \((-8, -3)\) and \(2, 3\). Thus, \(x_1 = -8\), \(y_1 = -3\), \(x_2 = 2\), and \(y_2 = 3\).
03

Substitute the Values

Substitute the values into the slope formula: \(\begin{align*}m &= \frac{y_2 - y_1}{x_2 - x_1} \&= \frac{3 - (-3)}{2 - (-8)}\end{align*}\).
04

Simplify the Expression

Further simplify the expression: \(\begin{align*}m &= \frac{3 + 3}{2 + 8} \&= \frac{6}{10}\end{align*}\).
05

Simplify the Fraction

Divide both the numerator and the denominator by their greatest common divisor, which is 2: \(m = \frac{6}{10} = \frac{3}{5}\). Thus, the slope of the line is \(\frac{3}{5}\).

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 Formula
The slope formula is key to understanding how steep a line is. It tells us how much the line rises or falls for every unit it moves horizontally. The formula for slope, often noted as \( m \), is given by:\[m = \frac{y_2 - y_1}{x_2 - x_1}\]Here:
  • \( x_1, y_1 \) are the coordinates of the first point on the line,
  • \( x_2, y_2 \) are the coordinates of the second point.
Using the formula, you can find the change in the vertical direction (\( y \)) and divide it by the change in the horizontal direction (\( x \)). This ratio gives the slope of the line.
Coordinates
Coordinates are used to pinpoint the exact location of a point on a graph. They come in pairs, written as \((x, y)\), and represent positions on the x-axis (horizontal) and y-axis (vertical), respectively.For example, the point \((-8, -3)\) means:
  • The point is 8 units left of the origin on the x-axis because of the negative sign.
  • It is 3 units down on the y-axis for the same reason.
These coordinate points help us determine where the line starts and ends, which is essential for calculating slope using the formula.
Simplifying Fractions
Simplifying fractions makes them easier to understand and work with. A fraction is simplified when it has the smallest possible numbers on the top (numerator) and bottom (denominator).For instance, when you have the fraction \(\frac{6}{10}\), it's not in its simplest form. By dividing both numbers by 2, you reduce it to \(\frac{3}{5}\). Simplifying shouldn't change the value of the fraction, just make it as simple as possible. This reduced form of fractions provides a clearer picture of the slope.
Greatest Common Divisor
The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder.To simplify fractions like \(\frac{6}{10}\), you need the GCD of 6 and 10, which is 2. Here's how it works:
  • List the factors of 6: 1, 2, 3, 6.
  • List the factors of 10: 1, 2, 5, 10.
  • Identify the largest number they both have: 2.
Using the GCD, divide both the numerator and denominator to simplify the fraction, making it easier to work with in problems.

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 equation. Check your solution. $$ 11-2 y=5 $$

Solve each equation. Check your solution. $$ \frac{1}{3} x-4=1 $$

Solve: \(5(x+4)=x+4\) \(\begin{array}{ll}{\text { Step } 1 : 5 x+20} & {=x+4} \\ {\text { Step } 2 :} & {4 x+20=4} \\ {\text { Step } 3 :} & {4 x=24} \\ {\text { Step } 4 :} & {x=6}\end{array}\) Which is the first incorrrect step in the solution shown above? A. Step 4 B. Step 3 C. Step 2 D. Step 1

You can graph inequalities by using the SHADE (command located in the DRAW menu. Enter two functions. \(\bullet\) The first function defines the lower boundary of the shaded region. If the inequality is " \(y \leq,\) use the Ymin window value as the lower boundary. \(\bullet\) The second function defines the upper boundary of the region. If the inequality is " \(y \geq,\) "use the Ymax window value as the upper boundary. Graph each inequality. $$ y \leq-2 x-4 $$

Graph each function. Identify the domain and range. \(h(x)=|-x|\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.