/*! 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 34 Use the given conditions to writ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 34

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-5)\) and \((6,-5)\)

Short Answer

Expert verified
The equations of the line in both point-slope form and slope-intercept form is \(y = -5\), which is a horizontal line at -5 on the y-axis.

Step by step solution

01

Calculate the Slope of the Line

The slope of a line (m) passing through two known points \((x_1,y_1)\) and \((x_2,y_2)\) is calculated by the formula \( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \). Applying this formula to the given coordinates, we get \( m = \frac{{-5 - (-5)}}{{6 - (-2)}} = 0 \). From here we can see that the slope is 0, which means the line is horizontal.
02

Write the Equation in Point Slope Form

The point-slope form of a line's equation is given by \(y - y_1 = m(x - x_1)\). Here, \(m\) is the slope and \(x_1, y_1\) are the coordinates of a point on the line. We can use one of our given points and the calculated slope for this form, i.e., \(y - (-5) = 0(x - (-2))\), which simplifies to \(y = -5\).
03

Write the Equation in Slope Intercept Form

The slope-intercept form of a line's equation is given as \(y = mx + c\), where m is the slope and c is the y-intercept. In this case, as the line is horizontal and the y coordinate remains constant while the x coordinate changes, the y-intercept is -5. So the equation becomes \(y = 0x - 5\) which simplifies to \(y = -5\).

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!

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

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ x^{2}+y^{2}=49 $$

If \(f(x+y)=f(x)+f(y)\) and \(f(1)=3,\) find \(f(2), f(3)\) and \(f(4) .\) Is \(f(x+y)=f(x)+f(y)\) for all functions?

Does \(f(x)\) mean \(f\) times \(x\) when referring to a function \(f ?\) If not, what does \(f(x)\) mean? Provide an example with your explanation.

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}-10 x-6 y-30=0 $$

Suppose that a function \(f\) whose graph contains no breaks or gaps on \((a, c)\) is increasing on \((a, b),\) decreasing on \((b, c)\) and defined at \(b\). Describe what occurs at \(x=b\). What does the function value \(f(b)\) represent?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

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.