Question

Find the value of r in (4, r), (r, 2) so that the slope of the line containing them is -5/3

Answer 1

r = 7

Explanation:

looking at the slope -5/3, -5 is the change in y and 3 is the change in x. so, we have to start from the point ( 4 , r ) and get to the next point ( r , 2 ) by using the given slope. we would first add 3 to our x value in the first point since that's our change in x and we would get r = 7. then we can substitute that in the other point and it works perfectly.

i hope this helps :)

Answer 2

`\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{r})\qquad (\stackrel{x_2}{r}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-r}{r-4}=\stackrel{\stackrel{given}{\downarrow }}{-\cfrac{5}{3}}\implies 3(2-r)=-5(r-4) \\\\\\ 6-3r=-5r+20\implies 6+2r=20\implies 2r=14\implies r=\cfrac{14}{2}\implies r=7`