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Answer:
Step-by-step explanation:
x - 8y = 16
Write in slope-intercept form: y = mx + b
-8y = -x + 16
Divide the entire equation by (-8)
[tex]y =\dfrac{-1}{-8}x+\dfrac{16}{-8}\\\\\\y=\dfrac{1}{8}x-2[/tex]
Parallel lines have slope. So, the slope of the required line = 1/8
[tex]y =\dfrac{1}{8}x+b\\\\\\[/tex]
(-8,2) is on the line. so, plugin the values in the above equation and find the y-intercept b
[tex]2=\dfrac{1}{8}*(-8)+b\\\\\\2=-1+b\\\\b = 2+1\\\\b = 3\\\\Equation \ of \ the \ required \ line:\\\\y=\dfrac{1}{8}x+3[/tex]
Answer:
[tex]\displaystyle x - 8y = -24\:or\:y = \frac{1}{8}x + 3[/tex]
Step-by-step explanation:
First off, convert this standard equation to a Slope-Intercept equation:
[tex]\displaystyle x - 8y = 16 \hookrightarrow \frac{-8y}{-8} = \frac{-x + 16}{-8} \\ \\ \boxed{y = \frac{1}{8}x - 2}[/tex]
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:
[tex]\displaystyle 2 = \frac{1}{8}[-8] + b \hookrightarrow 2 = -1 + b; 3 = b \\ \\ \boxed{\boxed{y = \frac{1}{8}x + 3}}[/tex]
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]
[tex]\displaystyle x - 8y = -24[/tex]
With that, you have your equation(s).
[tex]\displaystyle -x + 8y = 24[/tex]
*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.
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