a trainer for a professional football team keeps track of the amount of water players consume throughout practice. the trainer observes that the amount of water consumed is a linear function of the temperature on a given day. the trainer finds that when its 90 degrees the players consume about 220 gallons of water and when its 76 degrees the players consume about 178 gallons of water. write a linear function to model the relationship between the gallons of water consumed and the temperature.

Question

a trainer for a professional football team keeps track of the amount of water players consume throughout practice. the trainer observes that the amount of water consumed is a linear function of the temperature on a given day. the trainer finds that when its 90 degrees the players consume about 220 gallons of water and when its 76 degrees the players consume about 178 gallons of water. write a linear function to model the relationship between the gallons of water consumed and the temperature.

Answer 1

treat it as two ordered pairs (t, c) where t is temperature and c is consumption

so we have (90,220) and (76, 178)

slope = (220-178)(/(90-76) = 42/14 = 3

so:
c-220 = 3(t-90)
c = 3t - 270+220

c = 3t - 50

check:
if t = 90, c = 270-50 = 220
if t = 76, c = 228 - 50 = 178

Answer 2

To write a linear function that models the relationship between the gallons of water consumed and the temperature, we can use the slope-intercept form of a linear equation: y = mx + b.

Let's assign:
x as the temperature (in degrees)
y as the gallons of water consumed

We are given two data points: (90, 220) and (76, 178).

Using the slope-intercept form, we can find the slope (m) and the y-intercept (b):

Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (90, 220) and (76, 178):
m = (178 - 220) / (76 - 90)
= -42 / -14
= 3

Step 2: Substitute one of the points into the equation to solve for the y-intercept (b).

Using the point (76, 178):
178 = 3(76) + b
178 = 228 + b
b = 178 - 228
b = -50

Step 3: Write the linear function equation y = mx + b with the calculated slope (m) and y-intercept (b):

The linear function that models the relationship between the gallons of water consumed (y) and the temperature (x) is:
y = 3x - 50

Answer 3

To write a linear function that models the relationship between the gallons of water consumed and the temperature, we need two points. We have two data points: (90, 220) and (76, 178).

Let's define "temperature" as x and "gallons of water consumed" as y.

We can use the slope-intercept form of a linear function, which is y = mx + b, where m represents the slope and b represents the y-intercept.

First, let's find the slope (m) using the two data points:

m = (y₂ - y₁) / (x₂ - x₁)
m = (178 - 220) / (76 - 90)
m = -42 / -14
m = 3

Now, let's substitute one of the points and the slope into the equation to find the y-intercept (b):

y₁ = mx₁ + b
178 = 3 * 76 + b
178 = 228 + b
b = -50

Therefore, the linear function that models the relationship between the gallons of water consumed (y) and the temperature (x) is:

y = 3x - 50