Question

What is the slope of a line that is perpendicular to the line whose equation is 3x+2y=6?

Answer 1

Since this equation is already in standard form, there is no need to convert it. Standard form is Ax + By = C. In this equation, 3 = A, 2 = B, and 6 = C. From standard form, Ax + By = C equals negative A over B.

3x + 2y = 6

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`\displaystyle\ m = -(3)/(2)`

The slope cannot be simplified any more, so this would be the final answer.

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- Marlon Nunez

Answer 2

first, we can find the slope from the equation that is given buy solving the equation for y

3x+2y = 6

2y = 6-3x

y = 3-3/2x

y = -3/2x+3

now that the equation is in slope-intercept form, we can easily see that the slope of the given line is -3/2

perpendicular lines have slopes that are negative reciprocals, so we can just take the negative reciprocal of the slope we have

-3/2 → 3/2 → 2/3

the slope of the perpendicular line is 2/3

hope this helped