Question

A stretch of highway has a 4% uphill grade. This means that the road rises 1 foot for every 25 feet of horizontal distance. The beginning of the highway (x = 0) has an elevation of 2,225 feet. Write an equation for this stretch of roadway ini point-slope form.​

Answer 1

The equation for this stretch of roadway in point-slope form is
`y - 2225 = 0.04x`

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)`

In which
`(x_0,y_0)` 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`

The beginning of the highway (x = 0) has an elevation of 2,225 feet.

This means that
`(x_0,y_0) = (0,2255)`. So

`y - y_0 = m(x - x_0)`

`y - 2225 = 0.04(x - 0)`

`y - 2225 = 0.04x`

The equation for this stretch of roadway in point-slope form is
`y - 2225 = 0.04x`