Question

a new line is drawn through the point (-3,6) and perpendicular to the line with x-intercept (3,0) and y intercept (0,3) . what is the equation of this new line ?

Answer 1

The equation of the new line is
`y=x+9` or
`y-6=(x+3)`

Explanation:

step 1

Find out the slope of the line with x-intercept (3,0) and y intercept (0,3)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

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

step 2

Find the slope of the new line perpendicular 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)

`m_1*m_2=-1`

we have

`m_1=-1` ----> slope of the given line

so

`m_2=1` ---> slope of the new line

step 3

Find the equation of the new line in point slope form

`y-y_1=m(x-x_1)`

we have

`m=1`

`(x_1,y_1)=(-3,6)`

substitute

`y-6=(1)(x+3)`

`y-6=(x+3)` ----> equation in point slope form

Convert to slope intercept form

`y=mx+b`

isolate the variable y

`y=x+3+6`

`y=x+9`