Question

Find the equation of a line that has a y-intercept of 9 and is perpendicular to a line with the equation y = -4x + 13.

Answer 1

y =
`(1)/(4)` x + 9

Explanation:

the equation of a line in slope- intercept form is

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

given the line with equation

y = - 4x + 13 ← in slope- intercept form

with slope m = - 4

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-4)` =
`(1)/(4)`

given this line has a y- intercept of 9, then c = 9

y =
`(1)/(4)` x + 9 ← equation of perpendicular line

Answer 2

Our answer is y = 1/4x + 9.

`\Large\texttt{Explanation}`

We are asked to write an equation for a line that:

• is perpendicular to the line y = -4x + 13
• has a y-intercept at (0,9)

Since perpendicular lines have slopes that are opposite reciprocals, the line that's perpendicular to y = -4x + 13 has a slope of 1/4, which is the opposite reciprocal of -4.

To find the equation use the point-slope formula -

`\bf{y-y_1=m(x-x_1)}`

Plug in the data:

`\bf{y-9=\cfrac{1}{4}(x-0)}`

`\bf{y-9=\cfrac{1}{4}x}`

`\bf{y=\cfrac{1}{4}x+9}`

`\therefore` y = 1/4x + 9.