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Find the equation of the line that contains the point P(−3,1) and is perpendicular to the graph of 3x+9y=−8.

a) y=−3x−10
b) y=−1/3x+2
c) y=1/3x−4
d) y=3x+10

1 Answer

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Final answer:

The line perpendicular to the given line 3x + 9y = -8 that passes through the point P(-3, 1) has the equation y = 3x + 10.

The correct answer is option d) y=3x+10

Step-by-step explanation:

To find the equation of the line that is perpendicular to the given line and passes through the point P(-3, 1), we first need to find the slope of the given line. From the equation 3x + 9y = -8, we can rewrite it in slope-intercept form (y = mx + b) and find that the slope (m) is negative one-third (-1/3). Because perpendicular lines have slopes that are negative reciprocals of each other, the slope of our new line must be 3 (since it is the negative reciprocal of -1/3).Now that we have the slope of the perpendicular line, we can use point-slope form (y - y1 = m(x - x1)) where m is the slope and (x1, y1) is the point (-3, 1). Plugging in our values, the equation becomes y - 1 = 3(x + 3). Simplifying this, we get y - 1 = 3x + 9, and then y = 3x + 10 when we add 1 to both sides.

The correct equation for the line is y = 3x + 10, which corresponds to option d).

User Robert Parcus
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