Answer:
y = - 2x - 6 see below
Explanation:
You can start by finding the mid-point of your line and the slope of the line.
midpoint = 1/2 ( x₂ + x₁ ) , 1/2 ( y₂ + y₁ )
= 1/2 ( 2 + ⁻6 ) , 1/2 ( 0 + ⁻4 )
= 1/2 ( ⁻4 ) , 1/2 ( ⁻4 )
midpoint = - 2 , -2
Slope is rise (distance between y values) over run (distance between x values)
Rise = distance from - 4 to 0 is + 4
Run = distance from - 6 to +2 is 8
Slope is 4/8 or reduced down to 1/2. Since it is positive the line slopes upward left to right.
Slope is called m
Now find the slope of your bisecting perpendicular line
M (perpendicular) = - 1 / m (original line)
= -1 / (1/2) when dividing by a fraction, flip the fraction over. = - 2 (remember the negative value) since it is negative the line slopes downward from left to right.
Now that you know the slope of the perpendicular line and you know one point on that line is the midpoint of the original line, you can use the slope-intercept equation for a straight line to create your line equation.
y = mx + b where m is the slope and b is the y intercept
First find where the y intercept (b) is at for your new line by using the x and y values of the midpoint which is also a point on your new line.
-2 = -2(-2) + b or -2 = 4 + b or b = - 6
So you know your new line crosses the y axis at ( 0 , - 6 )
Now you can use the same formula to create the line equation of your new line.
y = mx + b with slope(m) = - 2 and b = -6
y = -2x - 6