SOLUTION: HOw is this solved? Write the slope form of the line that passes through the point A(-5,9) AND is perpendicular to the line with equation 2y-3x+5=0

Algebra ->  Graphs -> SOLUTION: HOw is this solved? Write the slope form of the line that passes through the point A(-5,9) AND is perpendicular to the line with equation 2y-3x+5=0      Log On


   

Question 736809: HOw is this solved?
Write the slope form of the line that passes through the point A(-5,9) AND is perpendicular to the line with equation 2y-3x+5=0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You ask, "HOW...?"
Good!

Here is how:
A line perpendicular to 2y-3x+5=0 will have a slope equal negative reciprocal of the slope of 2y-3x%2B5=0.

2y-3x+5=0
2y=3x-5
y=%283%2F2%29x-5%2F2
Slope of the given line is %283%2F2%29. The line perpendicular to the given line has a slope of -%282%2F3%29.

The line we want has slope -%282%2F3%29 and contains the point A(-5, 9). Let's use slope-intercept form to find the y-intercept*.
y=-%282%2F3%29x%2Bb
y%2B%282%2F3%29x=b
b=y%2B%282%2F3%29x
substitute the coordinate values for A,
b=9%2B%282%2F3%29%28-5%29
b=9-10%2F3
b=27%2F3-10%2F3
b=17%2F3
OR
b=5%262%2F3

Solution equation to question is highlight%28y=-%282%2F3%29x%2B17%2F3%29 OR highlight%28y=-%282%2F3%29x%2B5%262%2F3%29.

* You can choose point-slope form instead and do appropriate arithmetic steps. Also, you could use or put your equation into or use from standard form if you wished.