Question

find an equation for the line that has a x-intercept of 3 and is perpendicular to the graph of -2x+5y=6

Answer 1

`y=-(5)/(2)x+(15)/(2)`

or

`y=-2.5x+7.5`

Explanation:

step 1

Find the slope of the given line

we have

`-2x+5y=6`

isolate the variable y

`5y=2x+6`

`y=(2)/(5)x+(6)/(5)`

so

The slope is
`m=(2)/(5)`

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

`m_1*m_2=-1`

we have

`m_1=(2)/(5)`

so

`m_2=-(5)/(2)` ----> slope of the perpendicular line

step 3

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=-(5)/(2)`

`point\ (3,0)` ----> x-intercept

substitute

`y-0=-(5)/(2)(x-3)`

apply distributive property eight sides

`y=-(5)/(2)x+(15)/(2)`

or

`y=-2.5x+7.5`