Answer:
y = -3x - 4
Step-by-step explanation:
From the graph we see that the equation of a line is y = [tex]$ \frac{1}{3}x + 3 $[/tex]
Note that the product of the slopes of perpendicular lines = -1.
The general equation of the line is: y = mx + c, where m is the slope.
Since the slope of this line is 1/3, the slope of its perpendicular line should be -3.
Therefore, we arrive at the slope - one point form to determine the equation of the line.
That is: (y - y₁) = m(x - x₁)
where, (x₁, y₁) is the point passing through the given line.
Here, from the graph the point (0, 4) passes through it.
So, y - (-4) = -3(x - 0)
⇒ y + 4 = -3x
⇒ y = -3x - 4 which is the required equation of the line.
