MATH SOLVE

4 months ago

Q:
# the relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8400 ft, the liquid boils at 200.4 DegreesF. At an altitude of 4200 ft, the liquid boils at 206.7 degrees F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2100 ft?

Accepted Solution

A:

(a) getting the equation:

We'll assume that the altitude is represented by the x-axis and that the boiling point is represented by the y-axis.

Therefore, we have two given points:

(8400 , 200.4) and (4200 , 206.7)

Since the relation is linear, therefore, the graph forms of straight line with the general equation:

y = mx + c where m is the slope and c is the y-intercept.

First, we will calculate the slope:

m = (y2-y1) / (x2-x1) = (206.7 - 200.4) / (4200 - 8400) = -0.0015

Therefore, the equation of the line now is:

y = -0.0015x + c

Then, we will need to calculate the y-intercept. In order to do so, we will use any give point and substitute in the previously obtained equation as follows:

y = -0.0015x + c

206.7 = -0.0015(4200) + c

c = 213

Based on the above calculations, the equation of the line is:

y = -0.0015x + 213

(b) getting the boiling point at altitude = 2100 ft:

Now, in order to calculate the boiling point at altitude 2100, we will substitute in the equation of the line as follows:

y = -0.0015(2100) + 213 = 209.85 degrees Fahrenheit

We'll assume that the altitude is represented by the x-axis and that the boiling point is represented by the y-axis.

Therefore, we have two given points:

(8400 , 200.4) and (4200 , 206.7)

Since the relation is linear, therefore, the graph forms of straight line with the general equation:

y = mx + c where m is the slope and c is the y-intercept.

First, we will calculate the slope:

m = (y2-y1) / (x2-x1) = (206.7 - 200.4) / (4200 - 8400) = -0.0015

Therefore, the equation of the line now is:

y = -0.0015x + c

Then, we will need to calculate the y-intercept. In order to do so, we will use any give point and substitute in the previously obtained equation as follows:

y = -0.0015x + c

206.7 = -0.0015(4200) + c

c = 213

Based on the above calculations, the equation of the line is:

y = -0.0015x + 213

(b) getting the boiling point at altitude = 2100 ft:

Now, in order to calculate the boiling point at altitude 2100, we will substitute in the equation of the line as follows:

y = -0.0015(2100) + 213 = 209.85 degrees Fahrenheit