Write an equation of the line passing through each of the following pairs of points.

1 answer:

7 0

$\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{5}}}\implies \cfrac{-10}{-11}\implies \cfrac{10}{11}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{\cfrac{10}{11}}(x-\stackrel{x_1}{5})\implies y-7=\cfrac{10}{11}x-\cfrac{50}{11} \\\\\\ y=\cfrac{10}{11}x-\cfrac{50}{11}+7\implies y=\cfrac{10}{11}x+\cfrac{27}{11}$

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What is the measure of angle z in this figure?

astraxan [27]

Hello!

I've attached a photo for reference.

Lines A and B form straight angles, which measure 180 degrees. That means that -

m∠x + m∠y = 180°
m∠y + m∠z = 180°
m∠z + 43° = 180°
43° + m∠x = 180°

Since you're trying to find z, use the solvable equation with z in it:

m∠z + 43° = 180°
180 = z + 43
137 = z

Answer:
m∠z = 137°