Question

Which value of r gives the line passing through (3,2) and (r, -4) a slope of 3/2

Answer 1

`The\ point-slope\ formula:y-y_1=m(x-x_1)\\\\m=(3)/(2);\ (3;\ 2)\to x_1=3;\ y_1=2\\\\subtitute:\\\\y-2=(3)/(2)(x-3)\\\\y-2=(3)/(2)x-(9)/(2)\ \ \ \ |add\ 2=(4)/(2)\ to\ both\ sides\\\\y=(3)/(2)x-(5)/(2)\\\\(r;-4)\to x=r\ and\ y=-4\\\\subtitute:`


`-4=(3)/(2)r-(5)/(2)\ \ \ \ |add\ (5)/(2)\ to\ both\ sides\\\\-(8)/(2)+(5)/(2)=(3)/(2)r\\\\-(3)/(2)=(3)/(2)r\ \ \ \ \ |divide\ both\ sides\ by\ (3)/(2)\\\\-1=r\\\\\boxed{r=-1}`

Answer 2

label the points
x1=3
y1=2
x2=r
y2=-4
m=3/2
m=(y2-y1)/(x2-x1)
3/2= (-4-2)/r-3
3/2(r-3)= -6
3/2r-4.5= -6
3/2r= -1.5
r= -1