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wolverine [178]
3 years ago
5

Write an equation in point slope form for the line that passes through (-5,6) and (-3,-9).

Mathematics
1 answer:
Finger [1]3 years ago
8 0

\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\qquad
(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-9})
\\\\\\
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-9-6}{-3-(-5)}\implies \cfrac{-9-6}{-3+5}\implies -\cfrac{15}{2}


\bf \begin{array}{|c|ll}
\cline{1-1}
\textit{point-slope form}\\
\cline{1-1}
\\
y-y_1=m(x-x_1)
\\\\
\cline{1-1}
\end{array}\implies y-6=-\cfrac{15}{2}[x-(-5)]\implies y-6=-\cfrac{15}{2}(x+5)
\\\\\\
y-6=-\cfrac{15}{2}x-\cfrac{75}{2}\implies y=-\cfrac{15}{2}x-\cfrac{75}{2}-6\implies y=-\cfrac{15}{2}x-\cfrac{87}{2}

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4 years ago
Given the points (–3,k) and (2,0), for which values of k would the distance between the points be √34 ?
myrzilka [38]

Answer:

The values of k are 3 and -3

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

(-3,k)\\(2,0)  

d=\sqrt{34}

substitute

\sqrt{34}=\sqrt{(0-k)^{2}+(2+3)^{2}}

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6 0
4 years ago
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8 0
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We can solve this system by Gaussian elimination, first by multiplying the second equation in its entirety by 2, so that the x-terms will cancel.

We have 
16x-10y=10
and 
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The last equation is rewritten as -16x-12y=12.

Now, we cancel the x-terms.

16x-10y=10
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We have our value for y, so we just plug this back into any of the original equations to get x.

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