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3 years ago

What is the slope of a line with endpoints (2,3) and (6,8)?

Mathematics

2 answers:

horsena [70]3 years ago

5 0

Answer: $\dfrac{5}{4}$

Step-by-step explanation:

The slope of a line passing through (a,b) and (c,d) is given by :-

$m=\dfrac{d-b}{c-a}$

The given points : (2,3) and (6,8)

Then, the slope of the line passing through (2,3) and (6,8) is given by :-

$m=\dfrac{8-3}{6-2}=\dfrac{5}{4}$

Hence, the slope of a line with endpoints (2,3) and (6,8) = $\dfrac{5}{4}$

Yuki888 [10]3 years ago

4 0

We don't need to graph the line. All we have to do is use our slope formula.

Answer is provided in the image attached.

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Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist

yuradex [85]

Answer:

0 < t < 5 is the required interval for the differential equation (t - 5)y' + (ln t)y = 6t to have a solution.

Step-by-step explanation:

Given the differential equation

(t - 5)y' + (ln t)y = 6t

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y' + [(ln t)/(t - 5)]y = 6t/(t - 5)

(ln t)/(t - 5) is continuous on the interval (0, 5) and (5, +infinity).

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Answer:

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