Find the equation of the line that is perpendicular to y=3x and passes through the point (4,-2)

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = 3x

Comparing with the slope intercept form, slope = 3

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line passing through (4,-2) is - 1/3

To determine the intercept, we would substitute m = - 1/3, x = 4 and

y = -2 into y = mx + c. It becomes

- 2 = - 1/3 × 4 + c = 4/3 + c

c = - 2 + 4/3 = - 2/3

The equation becomes

y = - x/3 - 2/3

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