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3 years ago

A line passes through the point, (−8,7) and has a slope of −5/4. Please help...

Mathematics

1 answer:

o-na [289]3 years ago

8 0

Answer:

5x + 4y + 12 = 0

Step-by-step explanation:

Start with the point-slope equation of a straight line: y - k = m(x - h):

Here we are given the point (h, k): (-8, 7) and the slope m = -5/4. Inserting this info into the equation give above, we get: y - 7 = (-5/4)(x + 8).

We must put this equation into "standard form" Ax + By + C = 0.

Multiply all three terms by 4 to remove fractions: 4y - 28 = -5(x + 8), or

4y - 28 + 5x + 40 = 0

Rearranging these terms, we get 5x + 4y + 12 = 0, which is the desired equation in standard form.

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The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the ∠BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠CAB is AC

∵ The opposite side to ∠CAB is BC

∵ AB = 13 units ⇒ hypotenuse

∵ CB = 12 units ⇒ opposite

∵ AC = 5 units ⇒ adjacent

- Let us find the trigonometry ratios of angle BAC

∵ m∠CAB is x

∵ $sin(x)=\frac{BC}{AB}$

∴ $sin(x)=\frac{12}{13}$

∴ $x=sin^{-1}(\frac{12}{13})$

∵ $cos(x)=\frac{AC}{AB}$

∴ $cos(x)=\frac{5}{13}$

∴ $x=cos^{-1}(\frac{5}{13})$

∵ $tan(x)=\frac{BC}{AC}$

∴ $tan(x)=\frac{12}{5}$

∴ $x=tan^{-1}(\frac{12}{5})$

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

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