Question

At the curb a ramp is 11 inches off the ground. The other end of the ramp rests on the street 55 inches straight out from the curb. Write a linear equation in slope-intercept form that relates the height y of the ramp to the distance x from the curb.

y = 5x + 11
y = -1/5x + 11
y = -1/5x + 55
y = 1/5x + 55

Answer 1

`y=-(1)/(5)x+11`

Explanation:

The slope intercept form of a line is given by
`y=mx+b`

Here m is the slope and b is the y intercept.

Now, the slope can be defined as the ratio of rise and run.

`slope=(rise)/(run)`

It has been given that at the curb a ramp is 11 inches off the ground. It means the rise is -11.

Now, other end of the ramp rests on the street 55 inches straight out from the curb. Hence, run is 55.

Therefore, the slope is given by

`m=(-11)/(55)\\\\m=-(1)/(5)`

Therefore, the linear equation is

`y=-(1)/(5)x+b`

Also, from the second condition, we have a point (55,0)

`0=-(1)/(5)\cdot55+b\\0=-11+b\\b=11`

Therefore, the linear equation is

`y=-(1)/(5)x+11`