Answer:
y = 3x + 2
Explanation:
1. Work out the gradient of the line segment: change in y/change in x: -2 - -6/ -8 - 4 = 4/-12 = -1/3
2. Work out the gradient of the perpendicular bisector: the gradient of the line segment and the perpendicular bisector should multiply to get -1. This means that we can do -1 ÷ -1/3 to work out the gradient which is 3
4. Find the midpoint of the line segment: (-8 + 4) ÷ 2 = -2, and (-2 + -6) ÷ 2 = -4, so the midpoint is (-2, -4)
3. The equation will be in the format y = 3x + c and will go through (-2, -4), so we can substitute those values into the equation to find c:
- y = 3x + c
- -4 = 3(-2) + c
- -4 = -6 + c
- c = -4 + 6
- c = 2
The equation of the line is y = 3x + 2
Hope this helps!