/*! 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 63 a. Rewrite the given equation in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 63

a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. $$8 x-4 y-12=0$$

Short Answer

Expert verified
The slope intercept form of the equation is \(y = 2x - 3\). The slope is 2 and the y-intercept is -3. To graph, start at the point (0, -3) and then go up 2 units and right 1 unit, then draw the line through these points.

Step by step solution

01

Rewrite in slope-intercept form

To rewrite \(8x - 4y -12 =0\) in slope-intercept form, isolate \(y\) on one side of the equation. This can be achieved by first subtracting \(8x\) from both sides, to get \(-4y = -8x + 12\). Then divide through by \(-4\) to get \(y = 2x -3\).
02

Identify the slope and y-intercept

The form \(y = mx + b\) gives us \(m\) as the slope and \(b\) as the y-intercept. From the equation \(y = 2x -3\), we can see that the slope \(m\) is 2 and the y-intercept \(b\) is -3.
03

Graph the linear function

First plot the y-intercept on the vertical axis at \(y = -3\). Then from this point, use the slope to find the next point on the line. The slope is 2, which as a fraction is \(2/1\), meaning move up 2 units and right 1 unit. Draw the line through these two points.

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

a. Use a graphing utility to graph \(f(x)=x^{2}+1\) b. Graph \(f(x)=x^{2}+1, g(x)=f\left(\frac{1}{2} x\right),\) and \(h(x)=f\left(\frac{1}{4} x\right)\) in the same viewing rectangle. c. Describe the relationship among the graphs of \(f, g,\) and \(h,\) with emphasis on different values of \(x\) for points on all three graphs that give the same \(y\) -coordinate. d. Generalize by describing the relationship between the graph of \(f\) and the graph of \(g,\) where \(g(x)=f(c x)\) for \(0

Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25\) and \((x-2)^{2}+(y+3)^{2}=36\).

The bar graph shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care. Find a linear function in slope-intercept form that models the given description. Each function should model the percentage of total spending, \(p(x),\) by A mericans \(x\) years after \(1950 .\) (GRAPH CAN'T COPY) In \(1950,\) Americans spent \(22 \%\) of their budget on food. This has decreased at an average rate of approximately \(0.25 \%\) per year since then.

You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller playgrounds by placing the fencing parallel to one of the sides. Express the area of the playground, \(A\), as a function of one of its dimensions, \(x\).

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(6,-4) \text { and }(4,-2)$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.