Question

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Answer 1

To determine the equation for the line that best fits the data, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Given that the line passes through the point (0, 0) and that it takes 180 seconds to boil 300 milliliters of liquid, we can use this information to find the slope of the line.

Slope (m) = change in y / change in x

In this case, the change in y is the change in boiling time, which is 180 seconds, and the change in x is the change in liquid volume, which is 300 milliliters.

Slope (m) = 180 seconds / 300 milliliters

Simplifying the slope, we get:

Slope (m) = 3/5 seconds/milliliter

Now that we have the slope, we can substitute it into the slope-intercept form equation and use the given point (0, 0) to find the y-intercept (b).

0 = (3/5)(0) + b

Since anything multiplied by 0 is 0, the equation becomes:

0 = 0 + b

Therefore, the y-intercept (b) is 0.

Now we can write the equation for the line:

y = (3/5)x + 0

Simplifying the equation, we get:

y = (3/5)x

So, the equation for the line that best fits the data is y = (3/5)x. This equation represents the relationship between the boiling time of the liquid (y) in seconds and the liquid volume (x) in milliliters.

Answer 2

`y=(3)/(5)x`

Step-by-step explanation:

As the duration of the boiling is dependent upon the volume of the liquid, the liquid volume is the independent variable, while the boiling time is the dependent variable. Therefore:

Let x be the liquid volume (in milliliters).

Let y be the boiling time of a liquid (in seconds).

As the line passes through the origin (0, 0), it signifies a direct proportion, which can be expressed by the equation y = kx, where k is the constant of proportionality.

Given it takes 180 seconds to boil 300 milliliters of liquid, then y = 180 when x = 300. Therefore, to find the value of k, substitute these values into the direct proportion equation:

`180=300k`

Solve for k by dividing both sides of the equation by 300:

`300k=180`

`(300k)/(300)=(180)/(300)`

`k=(180)/(300)`

Reduce the fraction to its lowest form by dividing the numerator and denominator by 60:

`k=(180/60)/(300/60)=(3)/(5)`

Therefore, the equation for the line of best fit is:

`y=(3)/(5)x`