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What is the equation of the line passing through each pair of points in standard form

a) P(2, 3) and Q(5, 6)
b) A(5, - 1) and B(1, 5)

User Pir Abdul
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1 Answer

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Answer: a) x - y = -1

b) 3x + 2y = 13

Explanation:

a) To find the equation of the line passing through points P(2, 3) and Q(5, 6), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the points on the line.

First, we need to find the slope of the line passing through P and Q. The slope, m, is given by:

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

where (x1, y1) = (2, 3) and (x2, y2) = (5, 6).

m = (6 - 3)/(5 - 2) = 1

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line passing through P and Q:

y - 3 = 1(x - 2)

Simplifying the equation, we get:

y - 3 = x - 2

y = x + 1

To convert this equation to standard form, we can rearrange the terms to get:

x - y = -1

Therefore, the equation of the line passing through points P(2, 3) and Q(5, 6) in standard form is x - y = -1.

b) To find the equation of the line passing through points A(5, -1) and B(1, 5), we can use the same method as in part (a).

The slope of the line passing through A and B is:

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

where (x1, y1) = (5, -1) and (x2, y2) = (1, 5).

m = (5 - (-1))/(1 - 5) = -3/2

Using the point-slope form of the equation of a line, we get:

y - (-1) = (-3/2)(x - 5)

Simplifying the equation, we get:

y = (-3/2)x + 13/2

To convert this equation to standard form, we can rearrange the terms to get:

3x + 2y = 13

Therefore, the equation of the line passing through points A(5, -1) and B(1, 5) in standard form is 3x + 2y = 13.

User Reptilicus
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