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)
![\begin{gathered} \sqrt[]{(x+6)^2_{}}=\pm\sqrt[]{51} \\ \text{x + 6 = }\pm\sqrt[]{51} \\ x\text{ = -6 }\pm\sqrt[]{51} \\ \text{x = }-6\pm7.14 \\ x\text{ = -6+7.14 = }1.14 \\ x\text{ = -6 - 7.14} \\ \text{x = -13.14} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csqrt%5B%5D%7B%28x%2B6%29%5E2_%7B%7D%7D%3D%5Cpm%5Csqrt%5B%5D%7B51%7D%20%5C%5C%20%5Ctext%7Bx%20%20%2B%20%206%20%20%3D%20%7D%5Cpm%5Csqrt%5B%5D%7B51%7D%20%5C%5C%20x%5Ctext%7B%20%20%3D%20%20-6%20%20%7D%5Cpm%5Csqrt%5B%5D%7B51%7D%20%5C%5C%20%5Ctext%7Bx%20%20%3D%20%7D-6%5Cpm7.14%20%5C%5C%20x%5Ctext%7B%20%20%3D%20-6%2B7.14%20%20%3D%20%7D1.14%20%5C%5C%20x%5Ctext%7B%20%3D%20-6%20-%207.14%7D%20%5C%5C%20%5Ctext%7Bx%20%3D%20-13.14%7D%20%5Cend%7Bgathered%7D)
