Question

What is the equation of the line that is perpendicular to the given line and has an x-intercept of -3?

Answer 1

`y=-(3)/(2)x-(9)/(2)`

Explanation:

Let the equation of the perpendicular line is,

y = mx + b

where m = slope of the line

b = y-intercept

From the graph, slope of the line passing through (0, -1) and (3, 1),

m' =
`(y_2-y_1)/(x_2-x_1)`

m' =
`(1+1)/(3-0)`

m' =
`(2)/(3)`

To get the slope (m) of this line we will use the property of perpendicular lines,

m × m' = (-1)

m ×
`(2)/(3)` = -1

m =
`-(3)/(2)`

Equation of the perpendicular line will be,

`y=-(3)/(2)x+b`

x-intercept of the line is (-3) therefore, point on the line is (-3, 0)

0 =
`-(3)/(2)(-3)+b`

b =
`-(9)/(2)=-4.5`

Equation of the line will be,

`y=-(3)/(2)x-(9)/(2)`