What is the equation of a line that is perpendicular to y = 3 x − 2 and passes through the point ( 6 , 8 )

1 answer:

8 0

The slope of the given line is 3. Therefore, the slope of any line perpendicular to y = 3x - 2 is the negative reciprocal of 3, which is m = -1/3.

Starting with the point-slope equation of a straight line, obtain the specific equation applicable here by substituting the givens: m = -1/3, h = 6 and k = 8):

y - k = m (x - h) becomes y - 8 = (-1/3)(x - 6) (answer).

This could, if you wish, be rewritten in some other format.

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Solve for x. Round to the nearest tenth, if necessary.

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Answer:

$\boxed {\boxed {\sf x \approx 1.9}}$

Step-by-step explanation:

We are asked to find x, a missing side in a triangle.

This is a right triangle because there is a small square in the corner representing a 90 degree or right angle. Therefore, we can use right triangle trigonometry. The three main functions are:

sinθ= opposite/hypotenuse
cosθ= adjacent/hypotenuse
tanθ= opposite/adjacent

Examine the triangle. We will use angle S, measuring 54 degrees, for theta. Side QR, measuring x, is opposite angle S. Side QS, measuring 2.3, is the hypotenuse because it is opposite the right angle. Since we have the opposite and hypotenuse, we will use sine.

$sin \theta = \frac {opposite}{hypotenuse}$

θ= 54
opposite= x
hypotenuse = 2.3

$sin (54)= \frac{ x}{2.3}$

We are solving for x, so we must isolate the variable. It is being divided by 2.3 The inverse operation of division is multiplication, so we multiply both sides by 2.3

$2.3* sin (54)= \frac{x}{2.3}*2.3$