Slope of y=-7 as x increases from 8 to infinity

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    Infinity Slope
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Discussion Overview

The discussion revolves around understanding the slope of the linear function represented by the equation \(y = -7\) as \(x\) increases from 8 to infinity. Participants explore the implications of this slope in the context of linear functions and their equations.

Discussion Character

  • Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant states that the function decreases by 7 units for every 1 unit increase in \(x\), indicating a slope of -7.
  • Another participant identifies the linear function form \(y = mx + b\) and prompts others to find the values of \(m\) and \(b\).
  • A participant expresses confusion about whether \(b\) is -7 and acknowledges the simplicity of the question.
  • It is confirmed by another participant that \(m = -7\) and encourages others to solve the equation based on this slope.
  • A suggestion is made to use the point-slope formula for a line, providing a method to express the line using a known point and the slope.
  • A participant expresses gratitude for the clarification and notes the helpfulness of the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the slope being -7, but there is some confusion regarding the values of \(m\) and \(b\) in the context of the linear function.

Contextual Notes

There is an implicit assumption that participants understand the basic concepts of linear functions and their equations, but some express uncertainty about specific terms and their meanings.

Who May Find This Useful

This discussion may be useful for students learning about linear functions, slopes, and the different forms of linear equations.

rootbarb
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The function that passes through (8,3) and every time x increases by 1 unit, the fuction decreases by 7 units
 
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It's a linear function so it has the form $y=mx+b$. Can you find $m$ and $b$?
 
Is it stating that b is -7? I know y=mx+b but this question sounds so simple has me confused.
 
$m$ = $-7$. Do you see why $m=-7$? Can you solve it now?
 
Another formula for a line you may find useful here is the point-slope formula:

$$y=m\left(x-x_1\right)+y_1$$

where $\left(x_1,y_1\right)$ is a known point on the line and $m$ is the slope. :)
 
Thanks! Now I understand, def. noting both of your posts in my notepad :) This site is awesome!
 

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