What is the equation of the line that passes through the points (−3, 2) and (−5, 8)?

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

3 0

Answer:

The equation of the line is y = -3x - 7

Step-by-step explanation:

To find the equation of the line, we first need the slope. We can get that by using the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (8 - 2)/(-5 - -3)

m = (8 - 2)/(-5 + 3)

m = 6/-2

m = -3

Now that we have the slope, we use the slope and the given point in point-slope form. Then we solve for y.

y - y1 = m(x - x1)

y - 2 = -3(x + 3)

y - 2 = -3x - 9

y = -3x - 7

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Step-by-step explanation:

Right Triangles

In right triangles, where one of its internal angles measures 90°, the trigonometric ratios are satisfied.

We have completed the figure below with the missing internal angle A that measures A = 90° - 29° = 61° because the lines marked with an arrow are parallel.

Given the internal angle A, we can relate the unknown side of length x with the known side length of 500 ft, the hypotenuse of the triangle. We use the sine ratio:

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