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1 year ago

15. Write the slope-intercept form of the line described in the following:Parallel to 4x + 5y=20and passing through (12,4)

Mathematics

1 answer:

Amiraneli [1.4K]1 year ago

3 0

Problem

Write the slope-intercept form of the line described in the following:

Parallel to 4x + 5y=20

and passing through (12,4)

Solution>

For this case we need to have the same slope, and if we write the equation given we see:

5y = 20 -4x

y = 4 -4/5 x

then the slope m = -4/5

and we also know a point given x= 12, y= 4 and we can do the following:

4 = -4/5 (12) +b

4 = -48/5 + b

And if we solve for the intercept we got:

b= 4 +48/5= -28/5

And our equation would be given by:

y = -4/5 x -28/5

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Answer:

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Step-by-step explanation:

This question is incomplete; here is the complete question.

A train traveled from station A to station B at an average speed of 80 kilometers per hour and then from station B to station C at an average of 60 kilometers per hour. If the train did not stop at station b, what was the average speed at which the train traveled from station A to C?

(i). The distance that the train traveled from station A to station B was 4 times the distance that train traveled from station B to station C.

(ii). The amount of time it took to the train to travel from station A to station B is 3 times the amount of time that it took the train to travel from station B to station C.

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So the distance between Station A and station B = 4x km

Therefore, time to travel the distance x km with 80 km per hour = $\frac{\text{Distance traveled}}{\text{Speed}}$

= $\frac{4x}{80}$

Similarly time taken to travel between station B and station C with speed 60 km per hour = $\frac{x}{60}$ km per hour

Now average speed between station A and station C = $\frac{\text{Total distance between station A and station C}}{\text{time taken to travel}}$

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Therefore, time taken by the train between station A and B = 3t

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= 80 × 3t

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= 60t

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= $\frac{300t}{4t}$

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