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3 years ago

What is the slope of the line through (-10,1)(−10,1)left parenthesis, minus, 10, comma, 1, right parenthesis and (0,-4)(0,−4)

Mathematics

1 answer:

iris [78.8K]3 years ago

4 0

Answer:

$- \frac{1}{2}$

Step-by-step explanation:

We have to find the slope of the line through the points (-10,1) and (0,-4).

We know the formula of slope of a straight line when two different points on the line are known to be ( $x_{1}, y_{1}$ ) and ( $x_{1}, y_{1}$ ) is given by $[\frac{y_{1} - y_{2} }{x_{1} - x_{2}}]$ .

Therefore, in our case ( $x_{1}, y_{1}$ ) ≡ (-10,1) and ( $x_{1}, y_{1}$ ) ≡ (0,-4)

Therefore, the slope is $\frac{1 - (- 4)}{- 10 - 0} = - \frac{1}{2}$ (Answer)

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$k = \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(1)(13) } }{2(1)} \\ = \frac{ - 5 \pm \sqrt{25 - 52} }{2} \\ = \frac{ - 5 \pm \sqrt{ - 27} }{2} \: \: \: \: \: \: \\ = \frac{ - 5 \pm3 \sqrt{3} \: i}{2} \: \: \: \: \: \:$

Separate the solutions

$k_1 = \frac{ - 5 + 3 \sqrt{3} \: i }{2} \: \: \: \: or \\ k_2 = \frac{ - 5 - 3 \sqrt{3} \: i}{2}$

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Separate the real and imaginary parts

We have the final answer as

$k_1 = - \frac{5}{2} + \frac{3 \sqrt{3} }{2} \: i \: \: \: \: or \\ k_2 = - \frac{5}{2} - \frac{3 \sqrt{3} }{2} \: i$

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