Question

Help ASAP lines a and b are perpendicular. The equation of like a is y=1/3x+3 what is the equation of line b

Answer 1

y = -3x - 4

Explanation:

From the graph we see that the equation of a line is y =
`$  (1)/(3)x + 3 $`

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.