Question

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

Answer 1

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

Answer 2

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

$-4=\frac{3}{2}r-\frac{5}{2}\ \ \ \ |add\ \frac{5}{2}\ to\ both\ sides\\\\-\frac{8}{2}+\frac{5}{2}=\frac{3}{2}r\\\\-\frac{3}{2}=\frac{3}{2}r\ \ \ \ \ |divide\ both\ sides\ by\ \frac{3}{2}\\\\-1=r\\\\\boxed{r=-1}$