Question

The ordered pairs below represent a linear function: (3/4 , 6 1/4) , (1 1/4 , 7 3/4) , (x , y)

which values could be the values of x and y ?

Answer 1

Answer with explanation:

It is given that , ordered pair ,
`((3)/(4),6(1)/(4)),(1(1)/(4),7(3)/(4)),(x,y)` Represents a linear function.

If these three points are col linear slope between two points must be same.

Slope between two points
`(x_(1),y_(1)){\text{and}},(x_(2),y_(2))`

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m_(1)=(7(3)/(4)-6(1)/(4))/(1(1)/(4)-(3)/(4))=((6)/(4))/((2)/(4))=(6)/(2)=3\\\\ m_(1)=(y-6(1)/(4))/(x-(3)/(4))\\\\3=((4y-25)/(4))/((4x-3)/(4))\\\\12 x-9=4 y-25\\\\ 12 x- 4y-9+25=0\\\\ 12 x-4 y +16=0\\\\ 3 x -y +4=0\\\\  m_(1)=(y-7(3)/(4))/(x-1(1)/(4))\\\\3=((4y-31)/(4))/((4x-5)/(4))`

→3 × (4 x-5)=4 y-31

12 x - 15 = 4 y - 31

12 x- 4 y -15 +31=0

12 x- 4 y +16=0

→4×(3 x-y+4)=0

→3 x-y +4=0

All points lying on the line , 3 x - y +4=0, are the solution for values of x, and y.

Answer 2

Explanation:

(3/4 , 6 1/4) and (1 1/4 , 7 3/4) are two points on the line.

The change in y, going from the first point to the second, is 7 3/4 less 6 1/4, or 1 1/2. The corresponding change in x is 1 1/4 less 3/4, or 1/2.

Thus, the slope of this line is m = rise / run = (1 1/2) / 1/2, or 3.

If we chose x = 2, y would be 3(2), or 6: (2, 6)

If we chose x = 0, y would be 3(0), or 0: (0, 0)

These last two results represent two possible points on the line.