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We want to find the equation for a line that passes through the two points (-1,7) and (6,9).

  • First of all, remember what the equation of a line is:

                                    y = mx+b

Where, m is the slope and b is the y-intercept

First, let's find what m is, the slope of the line.

                                 m=   (9 - 7) / 6 - -1

                                 m=     2/7

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

                                  y=2/7x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(-1,7) means, When x of the line is -1, y of the line must be 7.

                         y=mx+b or 7=2/7 × -1+b

                                        or

                     solving for b: b=7-(2/7)(-1).

                                        b=51/7.

                      y=2/7x+51/7 (slopt intercept form)

             Now to get point slop form (y - y1) = m (x - x1)

                    by inserting value of m, x1 and y1

                      y - 7 = 2/7(x +1) (point slop form)

Now we get standard form, Ax+By=C

we can convert slop intercept form to standard form like this

                              y = 2/7x + 51/7


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