Question

What equation in slope-intercept form represents a line that passes through the point (2,3)

and is perpendicular to the line y−9=23(x+7)?

Answer 1

`y = ((-1)/(23) )x+(71)/(23)`

Explanation:

Given equation:
`y - 9 = 23(x + 7)`

Rewrite it in slope-intercept form:
`y = 23x + 161`

The slope of this line is 23.

The slope of the line perpendicular to it is the negative reciprocal of 23, which is
`(-1)/(23)`.

The line passes through the point (2, 3).

Substitute these values into the slope-intercept form (y = mx + b) and solve for the y-intercept (b):

`3=((-1)/(23) )(2)+b`

Simplify:
`3=(-2)/(23) +b`

Add
`(2)/(23)` to both sides:
`b = 3+(2)/(23) =(71)/(23)`

Therefore, the equation of the line that passes through (2, 3) and is perpendicular to
`y - 9 = 23(x + 7)` is:

`y = ((-1)/(23) )x+(71)/(23)`