Slope = 4/3, (-2, 11)

Mathematics

1 answer:

Lady_Fox [76]4 years ago

7 0

Answer:

y = $\frac{4}{3}$ x + $\frac{41}{3}$

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = $\frac{4}{3}$ , hence

y = $\frac{4}{3}$ x + c ← is the partial equation

to find c substitute (- 2, 11) into the partial equation

11 = - $\frac{8}{3}$ + c ⇒ c = $\frac{41}{3}$

y = $\frac{4}{3}$ x + $\frac{41}{3}$ ← equation of line

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Wewaii [24]

We know that:

$\sin (\theta_1)=-\frac{12}{13}$

There is also an interesting property that relates the sine and the cosine of an angle:

$\sin ^2(\theta_1)+\cos ^2(\theta_1)=1$

We can find the cosine of theta using this equation:

$\begin{gathered} \cos ^2(\theta_1)=1-\sin ^2(\theta_1) \\ \cos (\theta_1)=\sqrt{1-\sin^2(\theta_1)} \\ \cos (\theta_1)=\sqrt[]{1-(-\frac{12}{13})^2} \\ \lvert\cos (\theta_1)\rvert=\sqrt[]{1-\frac{144}{169}}=\sqrt[]{\frac{25}{169}} \\ \lvert\cos (\theta_1)\rvert=\frac{5}{13} \end{gathered}$

Since theta is in the third quadrant then its cosine must be a negative number so: