What is an equation of the line that passes through the point (-2,-3)(−2,−3) and is perpendicular to the line x+3y=24x+3y=24?

y = 3x + 3

Step-by-step explanation:

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

y = mx + c

Where

m represents the slope of the line.

c represents the y intercept.

The equation of the given line is

x + 3y = 24

3y = - x + 24

Dividing both sides of the equation by 3, it becomes

y = - x/3 + 8

Comparing with the slope intercept form, slope = - 1/3

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 (- 2, - 3) is 3

To determine the y intercept, we would substitute m = 3, x = - 2 and

y = -3 into y = mx + c. It becomes

- 3 = 3 × - 2 + c

- 3 = - 6 + c

c = - 3 + 6 = 3

The equation becomes

y = 3x + 3

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