What is the $x$-intercept of the line perpendicular to the line defined by $3x-2y = 6$ and whose $y$-intercept is 2?

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Step-by-step explanation:

3

because because

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.