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Write an equation in slope-intercept form that passes through the point (9, -9) and is perpendicular to 3x – 5y = 1. -2,-14,-6

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Final answer:

To find the equation of a line perpendicular to 3x - 5y = 1 and passing through the point (9, -9), we rearrange the given equation to slope-intercept form, find the negative reciprocal of the slope, and then use the point-slope form of a line.

Step-by-step explanation:

To find the equation of a line perpendicular to the given line, we need to find its slope and then use the point-slope form of a line. The given line has the equation 3x - 5y = 1, so we need to rearrange it to slope-intercept form by solving for y:

-5y = -3x + 1
y = (3/5)x - 1/5

The slope of the given line is 3/5. The slope of a line perpendicular to it will be the negative reciprocal of this slope, which is -5/3. Since we know the line passes through the point (9, -9), we can use the point-slope form to find its equation:

y - y1 = m(x - x1)

y - (-9) = -5/3(x - 9)

y + 9 = -5/3(x - 9)

y + 9 = -5/3x + 15

y = -5/3x + 15 - 9

The equation of the line that passes through the point (9, -9) and is perpendicular to 3x - 5y = 1 is y = -5/3x + 6.

User Etienne Dechamps
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