Question

Find the equation of a line that goes through point (100,-25) and is perpendicular to y=-25?

Answer 1

`x=100`

Explanation:

`y=-25`

`"is a horizontal line parallel to the x-axis and passing"`
`"through all points in the plane with a y-coordinate "-25`

`"a line perpendicular to it must be a vertical line"`

`"the equation of such a line is "x=c`

`"where c is the value of the x-coordinate the line"`
`"passes through"`

`"here the point is "(color(red)(100),-25)`

`"the equation of the perpendicular line is "x=100`

Answer 2

`y = 1/25x - 725`

Explanation:

Recall the standard equation of a line is;

`y = mx + c`

Also recall;

When its perpendicular;

`m_1 cdot m_2 = -1`

For the first equation;

Coordinate, `(100, -25)`

`x_1 = 100`

`y_1 = -25`

`m_1 = -25`

`m_1 cdot m_2 = -1`

`m_2 = -1/m_1`

Plugging in the value;

`m_2 = -1/(-25)`

`m_2 = 1/25`

Now the new equation of a line is;

`(y - y_1)/(x - x_1) = m_2`

Plugging in the values;

`(y - (-25))/(x - 100) = 1/25`

`(y + 25)/(x - 100) = 1/25`

Cross multiplying;

`(y + 25)25 = 1(x - 100)`

`25y + 625 = x - 100`

Collecting like terms;

`25y = x - 100 - 625`

`25y = x - 725`

`y = x/25 - 725 -> "Equation"`

`y = 1/25x - 725`