Question

Find the equation for the line that passes through -1,-2 and 4,3. Is the point 3,1 on the line

Answer 1

Answer:

• y = x -1
• no

Step-by-step explanation:

A graph quickly answers this question.

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The given points have a horizontal difference of 4-(-1) = 5 and a vertical difference of 3-(-2) = 5, so the slope of the line between them is ...

  m = Δy/Δx = 5/5 = 1

The point-slope form of the equation for a line can be written ...

  y = m(x -h) +k . . . . . for slope m through point (h, k)

Using the first point and the slope we found, we can write the equation as ...

  y = 1(x -(-1)) +(-2)

  y = x -1 . . . . . . . . . simplify; this is the equation of the line

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When we try the third point in this equation, we get ...

 y = 3 -1 = 2 ≠ 1 . . . . . the third point is not on the line