Question

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.

Answer 1

*attachment contains the omitted graph

Answer:

$y = -\frac{4}{3}x + 9$

Step-by-step explanation:

The equation that represents the path of the swimmer to the shoreline can be represented in the slope-intercept form, given as $y = mx + b$.

Where,

Slope (m) = the negative reciprocal of the slope of the shoreline, since it is perpendicular to it = ??

y-intercept (b) = ??

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

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} = \frac{3}{4}$.

Since the slope of the shoreline is ¾. The slope of the path of the swimmer would be the negative reciprocal of ¾.

The negative reciprocal of ¾ = -⁴/3.

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

Using the coordinate of the point of the swimmer (6, 1), and the slope of the path, we can find b, the y-intercept of the path.

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.

✅The equation that represents the path would be:

$y = -\frac{4}{3}x + 9$