Answer :
The value of r in (4,r),(r,2) so that the slope of the line containing them is [tex]\frac{-5}{3}[/tex] is 7
Solution:
Slope of the line which is passes through [tex]\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { and }\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right) \text { is }[/tex]
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] → (1)
From question given that two points are (4, r), (r, 2). Hence we get [tex]x_{1}=4 ; x_{2}=r ; y_{1}=r ; y_{2}=2[/tex]
By substituting the values in equation (1),
[tex]m=\frac{2-r}{r-4}[/tex] → (2)
Also given that slope that is m = [tex]\frac{-5}{3}[/tex], so on substituting the value of m in equation (2),
[tex]-\frac{5}{3}=\frac{2-r}{r-4}[/tex]
On simplifying,
-5r+20=6-3r
5r-3r=20-6
2r = 14
r =7
Hence value of r is 7.
