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Complete the point-slope equation of the line through (-5 4) and (1 6)

User Tan Duong
by
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1 Answer

1 vote

Answer:

y - 4 = 1/3(x + 5)

Explanation:

The general equation for the point-slope form of a line is given by:

y - y1 = m(x - x1), where

  • (x1, y1) is a point on the line,
  • and m is the slope of the line.

Step 1: To find the equation of the line through (-5, 4) and (1, 6), we first need to find the slope of the line using the slope formula, which is:

m = (y2 - y1) / (x2 - x1), where

  • (x1, y1) are one point on the line,
  • and (x2, y2) are another point on the line

We can allow (-5, 4) to be our (x1, y1) point and (1, 6) to be our (x2, y2) point:

m = (6 - 4) / (1 - (-5))

m = 2 / (1 + 5)

m = 2/6

m = 1/3

Now we can use the point-slope form of the equation with either of the two points.

  • Since we already used (-5, 4) as our (x1, y1) point, let's use it for the point-slope form:

y - 4 = 1/3(x - (-5))

y - 4 = 1/3(x + 5)

Thus, the point-slope equation of the line through (-5, 4) and (1, 6) is:

y - 4 = 1/3(x + 5)

User Ranieri Mazili
by
8.0k points

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