*attachment contains the omitted graph
Answer:
[tex] y = -\frac{4}{3}x + 9 [/tex]
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 [tex] y = mx + b [/tex].
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):
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} = \frac{3}{4} [/tex].
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:
[tex] y = -\frac{4}{3}x + 9 [/tex]
