Jason is a trainer for the Mamaroneck Jets football team. He keeps track of the amount of water that the players consume throughout practice. Jason observes that the amount of water consumed is linear to the temperature on each given day. Jason finds that when it is 90°F the players consume 220 gallons of water and when it is 76°F the players consume 178 gallons of water.
Write a linear equation to model the relationship between gallons of water consumed and the temperature.
You have two points: (90,220) and (76,178)
The slope is (220-178)/(90-76) = 3
So the point-slope equation is
y-178 = 3(x-76)
mr cherkasky wont be happy with cheating on his pom
To write a linear equation representing the relationship between gallons of water consumed and temperature, we need to find the equation of a line that passes through the points (90°F, 220 gallons) and (76°F, 178 gallons).
First, let's find the slope (m) using the formula:
m = (change in y) / (change in x)
m = (178 - 220) / (76 - 90)
m = -42 / -14
m = 3
The slope of the line is 3.
Next, let's use the point-slope form of a linear equation:
y - y1 = m(x - x1)
We can choose either of the given points to substitute for (x1, y1). Let's use the point (90°F, 220 gallons):
y - 220 = 3(x - 90)
Simplifying:
y - 220 = 3x - 270
Finally, let's rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
y = 3x - 270 + 220
y = 3x - 50
Therefore, the linear equation that models the relationship between gallons of water consumed (y) and temperature (x) is:
y = 3x - 50.
To write a linear equation that models the relationship between gallons of water consumed and temperature, we need to determine the equation of a straight line.
First, let's assign variables to the relevant quantities:
Let x be the temperature in degrees Fahrenheit.
Let y be the gallons of water consumed.
Now, let's use the given data to find the slope of the line:
When it is 90°F, the players consume 220 gallons of water, so one point on the line is (90, 220).
When it is 76°F, the players consume 178 gallons of water, so another point on the line is (76, 178).
The slope (m) of a line between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (178 - 220) / (76 - 90)
m = (-42) / (-14)
m = 3
Now that we have the slope, we can use it to find the y-intercept (b). We can choose any point on the line to do this. Let's use (90, 220) because it's one of the given data points.
Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the slope (m = 3) and the coordinates (x = 90, y = 220) into the equation to solve for b:
220 = 3(90) + b
220 = 270 + b
b = -50
Therefore, the linear equation that models the relationship between gallons of water consumed (y) and the temperature (x) is:
y = 3x - 50