Question

PLS HELP:( !! What is an equation of the line

that is perpendicular to the line
y= -2/3x-1 and passes through
the point (-4, 2)?

Answer 1

Y=3/2 because It passes through the point

Answer 2

`y = (3)/(2) x + 8`

Explanation:

The given equation is written in the form of y=mx+c (where m is the gradient and c is the y-intercept).

Thus, gradient of given equation= -⅔

The products of the gradient of perpendicular lines is -1.

(Gradient of line)(-⅔)= -1

Gradient of line

`= - 1 / ( - (2)/(3) ) \\ = (3)/(2)`

Hence, m=
`(3)/(2)`.

Subst. m=
`(3)/(2)`into the equation:

`y = (3)/(2) x + c`

To find the value of c, substitute a pair of coordinates into the equation:

When x= -4, y= 2,

`2 = (3)/(2) ( - 4) + c \\ 2 = - 6 + c \\ c = 2 + 6 \\ c = 8`

Thus, the equation of the line is
`y = (3)/(2) x + 8`.