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What is the equation of the line that is the parallel to x - 8y = 16 and passes throguh the point (-8, 2)

User Anzure
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2 Answers

3 votes

Answer:


\displaystyle x - 8y = -24\:or\:y = (1)/(8)x + 3

Step-by-step explanation:

First off, convert this standard equation to a Slope-Intercept equation:


\displaystyle x - 8y = 16 \hookrightarrow (-8y)/(-8) = (-x + 16)/(-8) \\ \\ \boxed{y = (1)/(8)x - 2}

Remember, parallel equations have SIMILAR RATE OF CHANGES, so ⅛ remains as is as you move forward with plugging the information into the Slope-Intercept Formula:


\displaystyle 2 = (1)/(8)[-8] + b \hookrightarrow 2 = -1 + b; 3 = b \\ \\ \boxed{\boxed{y = (1)/(8)x + 3}}

Now, suppose you need to write this parallel equation in Standard Form. You would follow the procedures below:

y = ⅛x + 3

- ⅛x - ⅛x

__________

−⅛x + y = 3 [We CANNOT leave the equation this way, so multiply by –8 to eradicate the fraction.]

−8[−⅛x + y = 3]


\displaystyle x - 8y = -24

With that, you have your equation(s).


\displaystyle -x + 8y = 24

*About this equation, INSTEAD of multiplying by –8, you multiply by its oppocite, 8. Now, you can leave it like this, but UNIVERSALLY, the A-term is positive, so you must multiply the negative out as well.

I am joyous to assist you at any time.

User WenHao
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2.6k points
7 votes

Answer:

Explanation:

x - 8y = 16

Write in slope-intercept form: y = mx + b

-8y = -x + 16

Divide the entire equation by (-8)


y =(-1)/(-8)x+(16)/(-8)\\\\\\y=(1)/(8)x-2

Parallel lines have slope. So, the slope of the required line = 1/8


y =(1)/(8)x+b\\\\\\

(-8,2) is on the line. so, plugin the values in the above equation and find the y-intercept b


2=(1)/(8)*(-8)+b\\\\\\2=-1+b\\\\b = 2+1\\\\b = 3\\\\Equation \ of \ the \ required \ line:\\\\y=(1)/(8)x+3

User IgorOK
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3.7k points