# How to solve this graph problem in WolframAlpha?

I need to input this problem in WolframAlpha:

Write an equation of the line containing the given point and parallel to the given line: $(8,-8)$, $7x+8y=5$.

The answer is $7x+8y=-8$ but I'm not sure how to format it so that I get that answer.

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Do you have to use WolframAlpha or are you allowed to use maths? – Michael Albanese Apr 18 '13 at 18:35

I used the guess until I get it right approach.

tangent line to 7x+8y=5 through (8,−8)


which resulted in:

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+1 Nice illustration. I thought you knew just the GAP, but it seems that I was completely wrong. :-) – Babak S. Aug 21 '13 at 8:35

You need only know that the slope of a line parallel to the given line is equal to the slope of the given line. Can you figure out the slope of you're given line?

$$7x + 8y = 5 \iff 8y = -7x + 5 \iff y = \dfrac{-7}{8}x + \dfrac 58$$

Now the original equation is in the form $$y = mx + b,\quad\text{where}\;\;m = -\dfrac 78\;\;\text{is the slope, and }\;\;b = \dfrac 58\;\;\text{is the y-intercept.}$$

Then you can use the point-slope form of an equation, and some algebra, to obtain the given answer, $$(y - y_0) = m(x - x_o)$$ where $(x_0, y_0) = (8, -8)$ and $m = -7/8$:

$$y-(-8) = -\dfrac 78(x - 8)$$ $$\iff y+ 8 = -\dfrac{7}{8} x + 7$$ $$\iff 8y + 64 = -7x + 56$$ $$\iff 8y + 7x = -8$$

To graph the equation using only the slope you found above and the given point, ask Wolfram Alpha for the "equation of the line with slope $-7/8$ and going through the point $(8, -8)$."

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To graph the line parallel to the given line, you simply "move" the given line "down" until it intersects the point $(8, -8)$. – amWhy Apr 18 '13 at 18:44