Question

How do you write the slope-intercept equation of the line perpendicular to y = 5/2 x - 2, which passes through the point (0, 2)?

Answer 1

See a solution process below:

Explanation:

The equation in the problem is in slope intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(5/2)x - color(blue)(2)`

Therefore the slope is: `color(red)(5/2)`

Next, let's call the slope perpendicular to this line `m_p`.

The slope of a perpendicular line is: `m_p = -1/m`

Substituting gives:

`m_p = -1/(5/2) = -2/5`

Because the point given in the problem has `0` for the `x` value this is the y-intercept for the perpendicular line. Substituting for `m_p = -2/5` and `2` for `b` into the slope-intercept formula gives:

`y = color(red)(-2/5)x + color(blue)(2)`