Luis's copy of Equation of a line parallel to a given line,

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Luis Hernandez 6 years, 4 months ago

Created this as a copy of Equation of a line parallel to a given line, .

Name	Status	Author	Last Modified
Equation of a line parallel to a given line,	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Equation of a line parallel to a given line,	draft	Luis Hernandez	30/11/2018 16:03
Hallar la ecuación de una recta paralela a una recta dada...	Ready to use	Luis Hernandez	14/12/2020 19:33

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Question statement

Find the equation of the straight line which:

Is parallel to $\displaystyle \simplify{{(b-d)/n2}x+{(c-a)/n2}y={(b*c-a*d)/n2}}$ .

Passes through the point $(\var{h},\var{k})$ .

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.

If you input $m$ as a fraction, put brackets ( ) around the fraction. For example, if your answer for $m$ is $\dfrac{-2}{3}$ and your answer for $c$ is $\dfrac{7}{5}$ , you should write $(-2/3)x+7/5$ .

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			Name	Type	Generated Value

a	integer	-2
c	integer	-6
b	integer	10
d	integer	9
g	rational	21/2
f	rational	1/4
h	integer	-6
s1	integer	-1
k1	rational	9
n1	number	1
n2	number	1
k	integer	-2
d1	integer	10

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Generated value: `integer`

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

The gradient $m$ will be the same as the gradient of the line $\displaystyle \simplify{{(b-d)/n2}x+{(c-a)/n2}y={(b*c-a*d)/n2}}$ , which is $\displaystyle m= \simplify{{b-d}/{a-c}}$ . We can calculate the constant term $c$ by noting that $y=\var{k}$ when $x=\var{h}$ .

Using this we get:

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

Hence the equation of the line is

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

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Luis's copy of Equation of a line parallel to a given line,

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Luis Hernandez 6 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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Luis's copy of Equation of a line parallel to a given line,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Luis Hernandez 6 years, 4 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`