Question

Write the point-slope form of the equation of the line through the given points.

9) through: (0, 1) and (−3, 2)
10) through: (5, −3) and (0, 3)
11) through: (1, 3) and (1, 1)
12) through: (0, 1) and (1, 5)

Answer 1

9. y -1 = -1/3(x -0) or y -1 = -1/3x

10. y +3 = -5/6(x -5)

11. x = 1

12. y -1 = 4(x -0) or y -1 = 4x

Explanation:

In every case, the slope is calculated from ...

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

Then that value is used in the point-slope equation:

y -y1 = m(x -x1)

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9) m = (2-1)/(-3-0) = 1/-3 = -1/3

y -1 = -1/3(x -0)

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10) m = (3 -(-3))/(0 -5) = 6/-5 = -5/6

y +3 = -5/6(x -5)

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11) m = (1 -3)/(1 -1) = -2/0 = undefined

No "y =" equation can be written for a line with undefined slope. The equation for a vertical line through these points with x-coordinate of 1 is ...

x = 1

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12) m = (5 -1)/(1 -0) = 4/1 = 4

y -1 = 4(x -0)