In this question, we are given a line. The standard equation of line is:
y = mx + b
Here, m is the slope, that is the difference of y values over the x values.
m = (y2 - y1) / (x2 - x1)
b is the y-intercept, where the value of x is zero.
If we see the line, x = 0, when y = -4. Hence, the y-intercept = b = -4
Also,
(x1, y1) = (0, -4)
(x2, y2) = (-4, 4)
m = [4 - (-4)]/ [-4 - 0]
m = 8/-4
m = -2
Hence, the equation of given line is
y = -2x - 4
The rule is: two lines are perpendicular if their slopes are negative reciprocal of each other.
In other words, two lines with slope m1 and m2 are perpendicular if
m1 = -1/m2
Now, the slope (m1) of the given line is -2. Hence, the slope (m2) of the perpendicular line would be m2 = 1/-(-2) = 1/2
Now, just put this value, we get
Y = 1/2 x - 4
As there is no solution closer to this one, I believe the 2nd answer Y = 1/2x + 3 would be correct.
