Question

A line passes through (-3, -2) and is perpendicular to 3x - 2y = 7.

What is the equation of the line in slope-intercept form?

Answer 1

When graphing this, the answer that I derived was y = -2/3x -4

Answer 2

Answer:
`y=(-2)/(3)x-4`

Explanation:

The given equation of line :

`3x-2y=7\\\\\Rightarrow\ y=(3)/(2)x-(7)/(2)`, comparing to the standard equation of line
`y=mx+c`, the slope of line =
`m= (3)/(2)`

Also, when two lines are perpendicular , then the product of their slope is -1.

Therefore, the slope of line perpendicular to the given line =
`(-1)/((3)/(2))=(-2)/(3)`

Now, the equation of the line passing from (-3, -2) with slope
`(-2)/(3)` is given by ;-

`(y-(-2))=(-2)/(3)(x-(-3))\\\\\Rightarrow\ y=(-2)/(3)(x+3)-2\\\\\Rightarrow\ y=(-2)/(3)x-4`

Hence, the equation of the line in slope-intercept form L

`y=(-2)/(3)x-4`