I really need help creating equations and finding the y-intercept and slope from these problems.
I need to hire a plumber. I have two friends that are recommending a plumber. One friend said for 3 hours of work the plumber charged $300. My other friend hired the same plumber and for 7 hours of work charged $500.
A water tank holding 200 gallons of water has sprung a leak. The leak releases 10 gallons of water every hour.
for the plumber, you have two points: (3,300) and (7,500)
The slope of the line joining these two points is (500-300)/(7-3) = 50
Now use the point-slope form to get the equation
y-300 = 50(x-3)
or
y = 50x + 150
now you can easily get the y-intercept (when x=0) as (0,150)
So the plumber charges $150 for a house call, plus $50/hr for labor
for the water tank, it is clear that the y-intercept is 200, since that's where the water level is at time t=0. Now, the volume of water changes by -10 every hour, so that's the slope.
y = 200 - 10t
you can find many examples of linear functions online.
Thank you
To create equations and find the y-intercept and slope, we need to understand the basic principles of linear equations.
1. Equation of a line:
In general, the equation of a line can be written in the form: y = mx + b, where "m" represents the slope of the line and "b" represents the y-intercept.
2. Slope (m):
The slope of a line is a measure of how steep it is. It can be calculated as the change in y divided by the change in x.
3. Y-intercept (b):
The y-intercept is the point where the line intersects the y-axis. It is the value of y when x is equal to zero.
Now let's solve the problems using these concepts:
Problem 1:
For the plumber's charges, we can use the information provided by your friends. Let's use x to represent the number of hours worked and y to represent the amount charged.
First, let's create two points based on the information given:
Point 1: (3 hours, $300)
Point 2: (7 hours, $500)
Using these points, we can calculate the slope (m) and the y-intercept (b).
Slope (m):
m = (change in y) / (change in x)
m = ($500 - $300) / (7 - 3)
m = $200 / 4
m = $50 per hour
Y-intercept (b):
We can plug one of the points into the equation y = mx + b to find the y-intercept.
Using Point 1: (3 hours, $300)
$300 = ($50 per hour * 3 hours) + b
$300 = $150 + b
b = $300 - $150
b = $150
So, the equation for the charges of the plumber is:
y = $50x + $150
Problem 2:
For the leaking water tank, let's use x to represent the number of hours and y to represent the amount of water in the tank.
The initial amount of water is 200 gallons, and the leak releases 10 gallons per hour.
The equation for the amount of water in the tank over time can be written as:
y = mx + b
where m represents the rate of water leakage and b represents the initial amount of water.
Since the leak releases 10 gallons per hour, the slope (m) is -10 (negative because it represents a decrease in water).
Y-intercept (b) is the initial amount of water in the tank, which is 200 gallons.
So, the equation for the amount of water in the tank is:
y = -10x + 200
By understanding the concepts of slope, y-intercept, and linear equations, we can solve problems like these and create equations accordingly.