What is the slope of each line

Question

Line 1 contains the points 0,-1 and 3,1. It is perpendicular to the line 2 that contains the point -1,2. What is the slope of each line?

Answer 1

(0,-1), (3,1) have a line through them with slope

= the difference in y values divided by the difference in x values

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

= (1+1)/(3-0)

= 2/3 = slope of Line 1

perpendicular line has slope

= -3/2 = slope of Line 2

(-1,2) is a point on the perpendicular line with equation

but is irrelevant to the slopes of Line 1 and Line 2,

but does provide information to calculate the equation of Line 2

y-2= (-3/2)(x+1) in point slope form

-3/2 = (y-2)/(x+1)

y= (-3/2)(x+1)+2

y= (-3/2)x -3/2+2

y = (-3/2)x+ 1/2 in slope intercept form

or

2y=-3x +1

3x+2y=1 in standard form

or

3x+2y-1=0 in general form