Question

If two lines are perpendicular and they are defined by the equations, y=2x-3 and y=ax+2, what is the value of a?

Answer 1

a = -
`(1)/(2)`

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x - 3 ← is in slope- intercept form

with slope m = 2

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(2)`

Thus the value of a in the equation y = ax + 2 is a = -
`(1)/(2)`