Step-by-step explanation:
I assume as "equation" we mean the slope-intercept form :
y = ax + b
"a" is the slope of the line (y coordinate change / x coordinate change when going from one point to another on the line). b is the y-intercept (the y value when x = 0).
we get the slope by finding the perpendicular slope of the first line.
the slope of the first line when going from (-3, -9) to (7, 8) :
x changes by + 10 (from -3 to +7).
y changes by + 17 (from -9 to +8).
so, that slope is 17/10.
the perpendicular slope is turning the original slope upside-down and flips the sign :
-10/17
so, a = -10/17
now, as we have only the slope and a point of the new line, we can use the point-slope form to stay and then transfer into the slope-intercept form.
y - y1 = a(x - x1)
where "a" is again the slope, and (x1, y1) is a point on the line
y - -6 = -10/17 × (x - -9)
y + 6 = -10/17 × (x + 9) = -10/17 × x - 90/17
y = -10/17 × x - 90/17 - 6 =
= -10/17 × x - 90/17 - 102/17 =
= -10/17 × x - 192/17
so, the equation is (in a maybe nicer way)
y = -1/17 × (10x + 192)
