Question 621067
The rational number {{{-2/3}}} is the same as (-2) divided by 3, and I could call it -2 over 3 too.
There are many ways to express it. It's like half a dozen and six.
{{{(-2)/3=-2/3=2/(-3)=(-1)*(2/3)}}}
The equation {{{y-1=-2/3}}}{{{(x-1)}}} represents the line with slope {{{-2/3}}} that passes through (1,1). (It's in point-slope form).
Any line parallel to that line will have slope {{{-2/3}}}.
The line with slope {{{-2/3}}} that passes through (3,5) has the equation
{{{y-5=-2/3}}}{{{(x-3)}}} (in point-slope form)
We can transform it into the slope-intercept form:
{{{y-5=-2/3}}}{{{(x-3)}}} --> {{{y-5=-2/3}}}{{{x-2/3}}}{{{(-3)}}} --> {{{y-5=-2/3}}}{{{x+2}}} --> {{{y=-2/3}}}{{{x+2+5}}} --> {{{y=-2/3}}}{{{x+7}}}