Answer:
x + 3y = 15
Step-by-step explanation:
Line is passing through the points ![(3, \:4) = (x_1,\:y_1)\:and\: (9, 2)=(x_2,\:y_2)](https://tex.z-dn.net/?f=%283%2C%20%5C%3A4%29%20%3D%20%28x_1%2C%5C%3Ay_1%29%5C%3Aand%5C%3A%20%289%2C%202%29%3D%28x_2%2C%5C%3Ay_2%29)
Slope of line (m)= (2 - 4)/(9 - 3) = -2/6 = -1/3
Equation of line in point-slope form is given as:
![y-y_1 =m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%20%3Dm%28x-x_1%29)
Plugging the values of
in the above equation we find:
![y-4 =-\frac{1}{3}(x-3)](https://tex.z-dn.net/?f=y-4%20%3D-%5Cfrac%7B1%7D%7B3%7D%28x-3%29)
![\implies 3y-12 =-x+3](https://tex.z-dn.net/?f=%5Cimplies%203y-12%20%3D-x%2B3)
![\implies x+ 3y =12+3](https://tex.z-dn.net/?f=%5Cimplies%20x%2B%203y%20%3D12%2B3)
![\implies \huge {\orange{\boxed{x+ 3y = 15}}}](https://tex.z-dn.net/?f=%5Cimplies%20%5Chuge%20%7B%5Corange%7B%5Cboxed%7Bx%2B%203y%20%3D%2015%7D%7D%7D)
This is the required equation of line in the form ![\red{\bold{ax + by = c}}](https://tex.z-dn.net/?f=%5Cred%7B%5Cbold%7Bax%20%2B%20by%20%3D%20c%7D%7D%20)
5. D
6.G
7.B
8.J
9.C
10.F
Sorry it took time.