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