Question

Hey there, I need help! Which line is perpendicular to the line shown in the graph?

Answer 1

y = -
`(1)/(2)` x + 1

Explanation:

calculate the slope m of the given line using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m =
`(1-(-3))/(2-0)` =
`(1+3)/(2)` =
`(4)/(2)` = 2

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

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

the equation of a line in slope- intercept form is

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

the only line with m = -
`(1)/(2)` , is

y = -
`(1)/(2)` x + 1 ← perpendicular line