To find the equation that models the relationship between the number of hours Luis rents the paddleboat (x) and the total cost (y), we can use the points given: (2, 30) and (4, 40).
First, we can find the slope (m) of the line using the two points. The slope is calculated as follows:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in our points (2, 30) and (4, 40):
- \(y_1 = 30\), \(x_1 = 2\)
- \(y_2 = 40\), \(x_2 = 4\)
Now calculate the slope:
\[ m = \frac{40 - 30}{4 - 2} = \frac{10}{2} = 5 \]
So, the hourly fee is $5, which is the slope of the line.
Next, we need to determine the y-intercept (b). We can use one of the points to find b. Let's use the point (2, 30):
The equation of a line in slope-intercept form is:
\[ y = mx + b \]
Plugging in the slope (m = 5) and the point (2, 30):
\[ 30 = 5(2) + b \]
Now solve for b:
\[ 30 = 10 + b\ b = 30 - 10 = 20 \]
Now we have both components of the equation: the slope (5) and the y-intercept (20). The total cost equation can be written as:
\[ y = 5x + 20 \]
Thus, the completed values for the equation based on the situation are:
- \(5\) for the coefficient of \(x\),
- \(20\) for the constant term.
So the answer is:
\[ y = 5x + 20 \]
5 answers