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Assoli18 [71]
2 years ago
11

What is the equation of the line that passes through the point (-6,-8) and has a slope of 1/3​

Mathematics
1 answer:
Arturiano [62]2 years ago
8 0

y + 8 = 1/3 (x+6)

With the given information, we can use the point-slope formula, , to write the equation of the line. Substitute values for the  , , and  in the formula to do so.

The  represents the slope, so substitute  in its place. The  and  represent the x and y values of one point the line intersects, so substitute -6 for  and -8 for . This gives the following answer and equation (just make sure to convert the double negatives into positives:  

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\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

Explanation

\frac{1}{a+bi}=c+di

Step 1

multiplicate by the conjugate

\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}

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\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\  \end{gathered}\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

I hope this helsp you

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