Lines in the Plane and Slope

Introduction

The simplest mathematical model for relating two variables is the linear equation $y=mx+b$. This equation is called Linear because its graph is a line. Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle m} is the slope and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (0,b)} is the y-intercept.

Finding the slope Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle m}

For instance, suppose you want to find the slope of the line passing through the distinct points Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (x_{1},x_{2})} and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (y_{1},y_{2})} .

$Slope={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}={\frac {y_{1}-y_{2}}{x_{1}-x_{2}}}$

Exercises Find the slope of the line passing through the distinct points below

1) $(-6,2)$ and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (3,20)}

Solution:
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 2}

2)$(3,-7)$ and $(-3,-7)$

Solution:
$0$

3)$(3,-2)$ and $(-3,1)$

Solution:
${\frac {-1}{2}}$

Writing the linear equation

Point-Slope Form of the Equation of a Line

The equation of the line with slope passing through the point Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_1,y_1)} is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y-y_1=m(x-x_1)}

Notes:

A vertical line goes through has equation of the form Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=a } where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a } is any constant.

This page were made by Tri Phan