Answer:
y = 255x + 6559
Step-by-step explanation:
Function Modeling
We have the following relationship between the minutes into the ride (x) and the elevation of the tram (y):
x={2,5,9,14}
y={7069,7834,8854,10129}
We first test if the relationship is linear or not.
A linear relationship is tested by calculating the slope from any pair of points.
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Selecting the first two points (2,7069) and (5,7834)
[tex]\displaystyle m=\frac{7834-7069}{5-2}=\frac{765}{3}[/tex]
m = 255
Selecting the first two points (5,7834) and (9,8854)
[tex]\displaystyle m=\frac{8854-7834}{9-5}=\frac{1020}{4}[/tex]
m=255
If we repeat the calculation with any pair of points, we get the same value for the slope, thus we can conclude the relationship is linear.
Using the point-slope form of the line:
y - k = m( x - h )
We select the point (2,7069)
y - 7069 = 255( x- 2 )
Operating:
y - 7069 = 255x - 510
Adding 7069:
y = 255x - 510 + 7069
y = 255x + 6559
