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Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2y = 6. Type your answer in the box provided or use the upload option to submit your solution.

Respuesta :

Rewrite the equation: 2y=x-6, y=x/2-3, so slope is 1/2 which is also the slope of the parallel line.
It will have the equation y=x/2+a where a is found by plugging in the given point: 4=-1+a, so a=5.
Therefore y=x/2+5. (This can also be written 2y=x+10 or x-2y+10=0)
JeanaShupp

Answer: [tex]x-2y=-10[/tex]

Step-by-step explanation:

Write [tex]x - 2y = 6[/tex] in intercept form([tex]y=mx+c[/tex]).

[tex]2y =x- 6[/tex]

[tex]y =dfrac{x- 6}{2}[/tex]

[tex]y =dfrac{x}{2}-3[/tex]

Here , slope of line  [tex]x - 2y = 6[/tex]  = [tex]m=\dfrac{1}{2}[/tex]  (Coefficient of x)

Also , the slope of two parallel lines are equal.  

Equation of line passing through point (a,b) and has slope m is given by :_

[tex](y-b)=m(x-a)[/tex]

Standard form of equation : [tex]Ax+By= C[/tex] ,where A is  positive integer a,d B and C be any integer.

Equation of the line parallel to line  [tex]x - 2y = 6[/tex]  and passing through (-2, 4)  will be :-

[tex](y-4)=\dfrac{1}{2}(x-(-2))\\\\ 2(y-4)=(x+2)\\\\ 2y-2(4)=x+2\\\\2y-8=x+2\\\\ x-2y=-8-2\\\\ x-2y=-10\ \ {\text{(Standard form)}}[/tex]  

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