Question

Find the value of x so that the line passing through the points will have the given slope: (x,6) and (10,-3) with a slope of -3/2.

Answer 1

`(x,6) \\ x_1=x \\ y_1=6 \\ \\ (10,-3) \\ x_2=10 \\ y_2=-3 \\ \\ \hbox{the slope: } m=(y_2-y_1)/(x_2-x_1)=(-3-6)/(10-x)=(-9)/(10-x) \\ \\ m=-(3)/(2) \\ \Downarrow \\ -(3)/(2)=(-9)/(10-x) \\ -(3)/(2)(10-x)=-9 \\ 10-x=-9 * (-(2)/(3)) \\ 10-x=3 * 2 \\ 10-x=6 \\ -x=6-10 \\ -x=-4 \\ \boxed{x=4}`