Find the equation of the line through the points (−2,5) and (4,9).
1 answer:
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Answer:
2x -3y = -19
Step-by-step explanation:
Taking the differences between the given points, we have ...
(Δx, Δy) = (4, 9) -(-2, 5) = (6, 4)
The equation of the line can be written ...
Δy·x -Δx·y = Δy·(x1) -Δx·(y1) . . . . . for point (x1, y1) on the line
4x -6y = 4(-2) -6(5) = -38
Dividing by 2 gives the standard form equation ...
2x -3y = -19
_____
<em>Additional comment</em>
The original equation 4x-6y=-38 satisfies the requirements of this problem. However, "standard form" requires the numbers in the equation be mutually prime (in addition to the problem requirements). That is, they must have no common factors. Hence, we must remove the common factor of 2 in order to have true "standard form."
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<span><u><em>Answer:</em></u>
sin (C)
<u><em>Explanation:</em></u>
<u>In a right-angled triangle, special trig functions can be applied. These functions are as follows:</u>
sin (theta) = </span>
<span>
cos (theta) = </span>
<span>
tan (theta) = </span>
<span>
<u>Now, let's check the triangle we have:</u>
<u>We have two options:</u>
<u>First option:</u>
5 is the hypotenuse of the triangle
4 is the side adjacent to angle B
Therefore, we can apply the <u>cos function</u>:
cos (B) = </span>
<span>
<u>Second option:</u>
5 is the hypotenuse of the triangle
4 is the side opposite to angle C
Therefore, we can apply the <u>sin function</u>:
sin (C) = </span>
<span>
Among the two options, the second one is the one found in the choices. Therefore, it will be the correct one.
Hope this helps :)
</span>
sin (C)
<u><em>Explanation:</em></u>
<u>In a right-angled triangle, special trig functions can be applied. These functions are as follows:</u>
sin (theta) = </span>
<span>
cos (theta) = </span>
<span>
tan (theta) = </span>
<u>Now, let's check the triangle we have:</u>
<u>We have two options:</u>
<u>First option:</u>
5 is the hypotenuse of the triangle
4 is the side adjacent to angle B
Therefore, we can apply the <u>cos function</u>:
cos (B) = </span>
<u>Second option:</u>
5 is the hypotenuse of the triangle
4 is the side opposite to angle C
Therefore, we can apply the <u>sin function</u>:
sin (C) = </span>
<span>
Among the two options, the second one is the one found in the choices. Therefore, it will be the correct one.
Hope this helps :)
</span>