Equation of a straight line

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Mohammad Rahman

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2 years, 8 months ago

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Mohammad Rahman 2 years, 8 months ago

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Equation of a straight line	Ready to use	Newcastle University Mathematics and Statistics	25/06/2022 13:18
Luis's copy of Equation of a straight line	draft	Luis Hernandez	30/11/2018 19:00
Hallar la ecuación de la recta que tiene pendiente conocida y pasa por un punto..	Ready to use	Luis Hernandez	14/12/2020 19:30
Maria's copy of Equation of a straight line	draft	Maria Aneiros	29/05/2019 05:08
Geradengleichungen	Ready to use	Ulrich Görtz	21/10/2020 14:56

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Question statement

Find the equation of the straight line which:

Has gradient $\displaystyle \simplify{{b-d}/{a-c}}$ .

Passes through the point $(\var{a},\var{b})$ .

Input your answer in the form $mx+c$ for suitable values of $m$ and $c$ .

Input $m$ and $c$ as fractions or integers as appropriate and not as decimals.

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			Name	Type	Generated Value

a	integer	-4
c	integer	-6
b	integer	-3
d	integer	7
g	rational	-23
f	rational	-5
s1	integer	-1
b1	integer	-3

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The equation of the line is of the form $y=mx+c$ .

You are given the gradient $\displaystyle m= \simplify{{b-d}/{a-c}}$ and we can calculate the constant term $c$ by noting that $y=\var{b}$ when $x=\var{a}$ .

Using this we get:

$\begin{eqnarray} \var{b}&=&\simplify[std]{({b-d}/{a-c}){a}+c} \Rightarrow\\ c&=&\simplify[std]{{b}-({b-d}/{a-c}){a}={(b*c-a*d)}/{(c-a)}} \end{eqnarray}$

Hence the equation of the line is

$y = \simplify[std]{({b-d}/{a-c})x+{b*c-a*d}/{c-a}}$

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Mohammad Rahman 2 years, 8 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Equation of a straight line

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mohammad Rahman 2 years, 8 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`