/*! 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 13 For each equation, find the slop... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 13

For each equation, find the slope. If the slope is undefined, state this. $$ 8 x=6 $$

Short Answer

Expert verified
The slope is undefined.

Step by step solution

01

Rewrite the Equation in Slope-Intercept Form

First, rewrite the given equation in a more familiar form. The equation is given as: 8x = 6.
02

Solve for x

Divide both sides of the equation by 8 to solve for x: \[ x = \frac{6}{8} \] Simplify the fraction: \[ x = \frac{3}{4} \]
03

Identify the Slope

The equation \( x = \frac{3}{4} \) represents a vertical line. Vertical lines have an undefined slope.

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.

Vertical Lines
When dealing with vertical lines on a graph, it's important to notice a few key characteristics. A vertical line runs straight up and down parallel to the y-axis.
This means its slope is not defined in the traditional sense. Why? Because the change in the x-coordinates along a vertical line is zero.
You can't divide by zero. So, we say the slope is undefined.
For instance, the equation 8x = 6 can be simplified to x = 3/4, which means that no matter what y value you have, x will always be 3/4. This is the hallmark of vertical lines in Cartesian coordinates.
  • Remember: Vertical lines always have an undefined slope.
  • These lines are written in the form x = a constant.
Slope-Intercept Form
The slope-intercept form is a common way to write the equation of a line. In general, it's written as y = mx + b, where:
  • m is the slope
  • b is the y-intercept
But sometimes, equations don't start in this form. For example, 8x=6 isn't in slope-intercept form. To find the slope, we need to change it into a recognizable format.
However, you should note that not all linear equations can be converted into slope-intercept form, especially if they represent vertical lines like x = 3/4. Such lines don't have a y-component to transform, directly showing they have an undefined slope.
Simplifying Fractions
Simplifying fractions is a fundamental skill in math. When we simplified 8x = 6 to x = 3/4, we performed a crucial step.
To simplify fractions:
  • Divide both the numerator and the denominator by their greatest common divisor (GCD).
  • In this case, the GCD of 6 and 8 is 2. Dividing both parts by 2, we get 3/4.
Understanding fraction simplification helps in various math problems and simplifies the process of interpreting results.
So here, x = 3/4 is simplified correctly, reinforcing the idea that this represents a vertical line with an undefined slope.

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

Assume that \(r, p,\) and \(s\) are nonzero constants and that \(x\) and \(y\) are variables. Determine whether each equation is linear. $$ \frac{x}{r}-p y=17 $$

Indicate which of the following equations have \(\left(-\frac{1}{3}, \frac{1}{4}\right)\) as a solution. a) \(-\frac{3}{2} x-3 y=-\frac{1}{4}\) b) \(8 y-15 x=\frac{7}{2}\) c) \(0.16 y=-0.09 x+0.1\) d) \(2(-y+2)-\frac{1}{4}(3 x-1)=4\)

Solve each equation graphically. Then check your answer by solving the same equation algebraically. $$ 3 x+7=4 $$

Solve graphically and then check by solving algebraically. $$ 4 x-1=3-2 x $$

Determine whether each equation is linear. Find the slope of any nonvertical lines. $$ 8 x+40=0 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.