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Find the equation of the line through point (5,4)

and perpendicular to y=−43x−2
. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12
).

User PemaGrg
by
8.0k points

1 Answer

4 votes

Answer:

y = 1/43x + 167/43.

Explanation:

y = -43x - 2 is in the slope-intercept form of a line, whose general equation is given by:

y = mx + b, where

  • (x, y) is any point on the line,
  • m is the slope,
  • and b is the y-intercept.

Thus, we want the equation of the other line to also be in slope-intercept form.

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 know.

Finding m2:

Thus, we can find m2, the slope of the other line, by plugging in -43 for m1:

m2 = -1/-43

m2 = 1/43

Thus, the slope of the other line is 1/43

Finding b:

We can find b, the y-intercept of the other line by plugging in (5, 4) for (x, y) and 1/43 for m in the slope-intercept form:

4 = 1/43(5) + b

(4 = 5/43 + b) - 5/43

167/43 = b

Thus, the y-intercept of the other line is 167/43.

Therefore, the equation of the line through the point (5, 4) and perpendicular to y = -43x - 2 is y = 1/43x + 167/43.

User Jason Marshall
by
8.8k points