Answer:
The equation for this stretch of roadway in point-slope form is ![y - 2225 = 0.04x](https://tex.z-dn.net/?f=y%20-%202225%20%3D%200.04x)
Step-by-step explanation:
Equation in point-slope form:
The equation of a line in point-slope form is given by:
![y - y_0 = m(x - x_0)](https://tex.z-dn.net/?f=y%20-%20y_0%20%3D%20m%28x%20-%20x_0%29)
In which
is the point and m is the slope.
A stretch of highway has a 4% uphill grade. This means that the road rises 1 foot for every 25 feet of horizontal distance.
This means that ![m = 0.04](https://tex.z-dn.net/?f=m%20%3D%200.04)
The beginning of the highway (x = 0) has an elevation of 2,225 feet.
This means that
. So
![y - y_0 = m(x - x_0)](https://tex.z-dn.net/?f=y%20-%20y_0%20%3D%20m%28x%20-%20x_0%29)
![y - 2225 = 0.04(x - 0)](https://tex.z-dn.net/?f=y%20-%202225%20%3D%200.04%28x%20-%200%29)
![y - 2225 = 0.04x](https://tex.z-dn.net/?f=y%20-%202225%20%3D%200.04x)
The equation for this stretch of roadway in point-slope form is ![y - 2225 = 0.04x](https://tex.z-dn.net/?f=y%20-%202225%20%3D%200.04x)