A wooden access ramp is being built to reach a platform that sits 45 inches above the floor. The ramp drops 3 inches for every 31-inch run.

-Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform.
y=?

-Find and interpret the​ x-intercept of the graph of your equation.
x is?

-Now interpret the​ x-intercept of the graph of your equation. Choose the correct answer below.
A.The ramp meets the platform this many inches from the floor.
B.The ramp meets the floor this many inches from the base of the platform.
C.The maximum rise is this many inches.
D.The length of the ramp is this many inches.

-Design requirements stipulate that the maximum run be 30feet ​(360 inches) and that the maximum slope be a drop of 1 inch for each 8 inches of run. Will this ramp meet the​ requirements? Explain. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A) The ramp does not meet design requirements. It has a run of nothing ___ ft.
B.The ramp does not meet design requirements. It has a rise of nothing ____ ft.
C. The ramp meets design requirements.

-What slope could be used to obtain the 45-inch rise and still meet design​ requirements?
m=?

1 answer

clearly, the height at x=0 is 45. So,

y = 45 - (3/31)x

The x-intercept, naturally, is how far away from the platform the ramp's height is zero.