A canoe rental shop is being built near a river. An equation of the line representing the river is y=1/4x+8. Each unit in the coordinate plane corresponds to 100 feet. Approximately how far is the canoe rental shop from the river? Round your answer to the nearest whole foot. The rental shop is at (-3,3).

412.3 feet

Step-by-step explanation:

To find the distance from the rental shop to the river, we need to use the formula of the distance between a point and a line:

distance(ax + by + c = 0, (x0, y0)) = |ax0 + by0 + c| / sqrt(a2 + b2)

putting the equation y = (1/4)x + 8 in the form ax + by + c = 0, we have a = 1/4, b = -1 and c = 8, and the point represents x0 = -3 and y0 = 3, so we have:

distance = |(1/4) * (-3) - 1*3 + 8| / sqrt( (1/4)^2 + (-1)^2)

distance = |-3/4 + 5| / 1.0308

distance = 4.25 / 1.0308 = 4.123 units

If each unit in the coordinate plane corresponds to 100 feet, the real distance is:

real distance = distance * 100 = 412.3 feet