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alexandr402 [8]
2 years ago
10

What is the slope of the line that passes through the points (1,7) and (-4,-8)?

Mathematics
2 answers:
frozen [14]2 years ago
7 0

Answer:

D) 3

Step-by-step explanation:

Given: The line passes through the points (1, 7) and (-4, -8)

Here we have to use formula to find the slope.

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

Here x1 = 1, y1 = 7, x2 = -4 and y2 = -8

Now plug in these values in the above formula, we get

slope = (-8 - 7) / (-4 - 1)

= -15/-5

slope (m) = 3

Therefore, the slope of the line is 3.

Answer: D) 3

Hope you will understand the concept.

Thank you.

Aleksandr [31]2 years ago
5 0

Answer:

D. 3

Step-by-step explanation:

To find the slope of a line, we can use the equation y2-y1/x2-x1=m or slope.

All we can do now is insert the values of the points into the equation.

-8-7/-4-1=m

-15/-5=m

3=m

Thus, the slope is 3.

Hope this helps!

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Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).
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Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

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x = 12/4

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df/dy = 2(y - 2) + 2y = 0

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4y = 4

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Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

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3 years ago
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