Question

Type an equation of any line perpendicular to these parallel lines.

Answer 1

The equation of any line perpendicular to these parallel lines is:

`y = -(1)/(4)x + b`, where b is any constant.

The slope of the parallel lines is 4, so the slope of the perpendicular line is its negative reciprocal, which is
`-(1)/(4)`.

To find the value of b, we can use the point-slope form of linear equations:

`y - y_1 = m(x - x_1)`

where m is the slope of the line and
`(x_1, y_1)` is a point on the line.

Let's choose the point (0, 1) on the perpendicular line. Substituting these values into the equation above, we get:

`1 - 1 = -(1)/(4)(0 - 0)`

0 = 0

This is a true statement, so our equation is correct.

Therefore, any line perpendicular to the parallel lines in the image has the equation:

`y = -(1)/(4)x + b`

where b is any constant.