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3 years ago

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What is an equation of the line that passes through the points (-6, -5) and (-3,0)? Put your answer in fully reduced form.

1 answer:

MrMuchimi3 years ago

6 0

Answer:

y = 5/3x +5

Step-by-step explanation:

The two-point form of the equation of a line is useful here.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

y = (0 -(-5))/(-3 -(-6))(x -(-6)) -5

y = 5/3(x +6) -5

y = 5/3x +5 . . . . slope-intercept form

5x -3y = -15 . . . .standard form

_____

There is no "fully reduced" form of the equation of a line. There are slope-intercept form, point-slope form, two-point form, standard form, general form, intercept form, and some others. We assume that "fully reduced" applies to any fractions in the equation. The "slope-intercept" form has a fraction, so perhaps that's the form that is required.

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1 year ago

when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four s

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Answer:

The stone would take approximately 10.107 seconds to fall 500 meters.

Step-by-step explanation:

According to the statement of the problem, the following relationship of direct proportionality is built:

$t \propto y^{1/2}$

$t = k\cdot t^{1/2}$

Where:

$t$ - Time spent by the stone, measured in seconds.

$y$ - Height change experimented by the stone, measured in meters.

$k$ - Proportionality constant, measured in $\frac{s}{m^{1/2}}$ .

First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:

$k = \frac{t}{y^{1/2}}$

If $t = 4\,s$ and $y=78.4\,m$ , then:

$k = \frac{4\,s}{(78.4\,m)^{1/2}}$

$k \approx 0.452\,\frac{s}{m^{1/2}}$

Then, the expression is $t = 0.452\cdot y^{1/2}$ . Finally, if $y = 500\,m$ , then the time is:

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago