Question

Write the equation of the line with a slope of 3/7 passing through the point (9, -2)

Answer 1

Use the point-slope form:
\[y-y_{0}=m(x-x _{0})\]
where m = 3/7, x0=9 and y0=-2
y+2=3/7(x-9)
7(y+2)=3x-27
7y+14=3x-27
In standard form: 3x-7y-41=0

Answer 2

There are two basic ways to write a line:

If have you a slope and a y-intercept: y=mx+b
If you have 2 points though: (y-k)=m(x-h)

That second one can look longer, but if you remember that x is before y in the alphabet and h is before k, it is actually really helpful.

So:

(y-k)=m(x-h)
y and x stay there, you just substitute in k, h, and m.

m is your slope: 3/7
k and h are (h,k) you point: (0,-2)

Therefore:

(y-(-2))=(3/7)(x-0)
y+2=(3/7)x
y+2=3x/7
y=(3x/7)-2