Write in point slope form an equation of the line through each pair of points (2,7) and (-4,1)

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Alannah Yang · Accepted Answer

Two points uniquely identify a line, and the formula we must use is the following: when given two points             (              x        1            ,              y        1            )       and             (              x        2            ,              y        2            )      , the line passing through both of them is                    y        -                  y          2                                      y          1                -                  y          2                      =                  x        -                  x          2                                      x          1                -                  x          2                    Plugging the values             (              x        1            ,              y        1            )        =          (      2      ,      7      )       and             (              x        2            ,              y        2            )        =          (      -      4      ,      1      )       into that formula, we get                    y        -        1                    7        -        1              =                  x        +        4                    2        +        4              ⇔                  y        -        1                    6              =                  x        +        4                    6              ⇔    y    -    1    =          (      x      +      4      )      Which can be brought into the standard form:      y    -    1    =    x    +    4    ⇔    y    =    x    +    5  You can easily check that this is the right solution, because for both points (2,7) and (−4,1) you have that the y coordinate equals the x one plus 5.

Write in point slope form an equation of the line through each pair of points (2,7) and (-4,1)

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