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2 years ago

Please help me on this

Mathematics

1 answer:

Morgarella [4.7K]2 years ago

4 0

to get the equation of any straight line, we simply need two points off of it, so hmm let's use the two points you see in the picture below from the provided table.

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}\implies \cfrac{5+1}{3}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{2}(x-\stackrel{x_1}{1}) \\\\\\ y+1=2x-2\implies y=2x-3$

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3 years ago

Point B has coordinates (1,2). The x-coordinate of point A is negative 8. The distance between point A and point B is 15 uni

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Answer:

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Step-by-step explanation:

Point B has coordinates (1,2) and the x-coordinate of point A is - 8.

Let us assume that the coordinates of point A are (-8,k).

Now, given that the point A is 15 units apart from point B.

Therefore, from the distance formula, we can write that

$\sqrt{(1 - ( -8))^{2} + (2 - k)^{2}} = 15$

Now,squaring both sides, we get

$(1 - ( -8))^{2} + (2 - k)^{2} = 225$

⇒ $(2 - k)^{2} = 225 - 9^{2} = 144$

⇒ 2 - k = ± 12

⇒ k = 14 or -10.

Therefore, the point A will be (-8,14) or (-8,-10). (Answer)

We know that the distance between two points on the coordinate plane ( $x_{1}, y_{1}$ ) and ( $x_{2}, y_{2}$ ) is given by

$\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$ .

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3 years ago

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Step-by-step explanation:

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