Explanation:
yes, so ?
an equation is like the given line :
y = (3/4)x - 10
2 expressions with an "=" (equal) sign between them.
it gives us a prescription what to do with one side, if we do something with the other, because both sides always need to be equal.
the given line is the summary of all points for which that equation is true.
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
so, we see the slope of the given line is 3/4. meaning that when x changes by 4 units, y changes by 3 units.
a perpendicular slope turns that y/x ratio upside-down and flips the sign.
in our case :
-4/3
therefore our equation looks like
y = -(4/3)x + b
to get b we use the coordinates of the given point :
8 = -(4/3)×-6 + b = 8 + b
b = 0
and our equation is
y = -(4/3)x