Question

A rope is tied to the top of a 4-meter-tall tree. Its other end is tied to the ground 1 meter away from the tree. What is an equation for the rope's height y at distance x from the tree, in standard form?

Answer 1

Answer:

y = -4x + 4, with x and y in meters

Step-by-step explanation:

To find an equation that represents the rope's height y at distance x from the tree, we can use two known pair of values x and y, and use them in the standard model of a linear equation:

y = ax + b

The pair of points we know are:

for x = 0, the rope's height is y=4 meters(this is the point where the tree's base is located, and the rope's height will be the tree's height)

for x = 1, the rope's height is y=0 meters (this is the point where the rope is tied to the ground)

Now, using these pair of points, we can find 'a' and 'b' in the equation model:

4 = a*0 + b -> b = 4

0 = a*1 + b -> a = -b = -4

So, the equation we want is:

y = -4x + 4, with x and y in meters