The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the shoreline. Write an equation that represents this path.

An equation that represents this path is described below in detail.

Step-by-step explanation:

The equalization that describes the pathway of the swimmer to the shoreline can be described in the slope-intercept pattern, given as.

Where,

Slope (m) = the adverse reciprocal of the incline of the shoreline, considering it is perpendicular to it = ??

y-intercept (b) = ??

Find the incline of the shoreline using, (0, 1) and (4, 4):

.

Considering the incline of the shoreline is ¾. The incline of the pathway of the swimmer would be the adverse reciprocal of ¾.

The adverse reciprocal of ¾ = -⁴/3.

The incline of the swimmer's path = -⁴/3.

Applying the coordinate of the position of the swimmer (6, 1), and the incline of the way, we can find b, the y-intercept of the way.

Substitute x = 6, y = 1 and m = -⁴/3 into y = mx + b, to find b.

Thus:

1 = (-⁴/3)(6) + b

1 = -8 + b

Add 8 to both sides

1 + 8 = b

9 = b

b = 9

Substitute m = -⁴/3 and b = 9 into y = mx + b.

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