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Write the equation for the line perpendicular to y=-1/9x+5 and passing through the point (7,10) in slope intercept form

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Answer:

y = 9x - 53

Explanation:

Relationship between the slopes of perpendicular lines:

The slopes of perpendicular lines are negative reciprocals of each other, as shown by the formula m2 = -1/m1, where

  • m2 is the slope of the line we're trying to find,
  • and m1 is the slope of the line we're given.

Identifying the slope of y = -1/9x + 5:

y = -1/9x + 5 is in the slope-intercept form of a line, whose general equation is given by:

y = mx + b, where

  • m is the slope
  • and b is the y-intercept.

Thus, the slope (i.e., m1) is -1/9.

Determining the slope of the other line:

Now we can find the slope of the other line (i.e., m2) by substituting -1/9 for m1 in the perpendicular slope formula:

m2 = -1 / (-1/9)

m2 = -1 * -9/1

m2 = 9

Thus, the slope of the other line is 9.

Finding the y-intercept of the other line:

Now we can find the y-intercept (b) of the other line by substituting 9 for m and (7, 10) for (x, y) in the slope-intercept form:

10 = 9(7) + b

(10 = 63 + b) - 63

-53 = b

Thus, the y-intercept of the other line is -53.

Writing the equation of the other line in slope-intercept form:

Therefore, y = 9x - 53 is the equation of the line perpendicular to y = -1/9x + 5 and passing through the point (7, 10) in slope-intercept form:

User Jonas Kongslund
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