An Electrician Charges $120 After 2 Hours Of Work And $190 After 4 Hours Of Work. Write A Linear Model That Represents The Total Cost.
Are you German? What's With All The Capitalization?
The lope of the line is (190-120)/2 = 35
y = 50 + 35x
slope and y-intercept
y=35x+50
there's 2 textbooks?? bc my classmates have different
To write a linear model that represents the total cost, we need to determine the relationship between the number of hours of work and the corresponding cost.
Here's how we can approach this:
Step 1: Define the variables:
Let's say:
- x represents the number of hours of work.
- y represents the total cost.
Step 2: Determine the slope, m:
To find the slope, we can use the formula:
m = (change in y) / (change in x)
We have two data points: (2, 120) and (4, 190). Using these points, we can calculate the change in y and change in x:
Change in y = 190 - 120 = 70
Change in x = 4 - 2 = 2
So, the slope is:
m = 70 / 2 = 35
Step 3: Determine the y-intercept, b:
To find the y-intercept, we can substitute the values of one of the data points into the equation (using the slope-intercept form) and solve for b.
Let's use the point (2, 120):
120 = 35(2) + b
120 = 70 + b
Now, isolate b:
b = 120 - 70 = 50
Step 4: Write the linear model using the slope-intercept form:
y = mx + b
Substituting the values we found earlier:
y = 35x + 50
Therefore, the linear model that represents the total cost is:
Total cost (y) = 35(number of hours of work, x) + 50