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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 ?

The ordered pairs below represent a linear function 34 6 14 1 14 7 34 x y which values could be the values of x and y class=

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Answer:

Step-by-step 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.

Answer with explanation:

It is given that , ordered pair ,[tex](\frac{3}{4},6\frac{1}{4}),(1\frac{1}{4},7\frac{3}{4}),(x,y)[/tex] Represents a linear function.

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

Slope between two points [tex](x_{1},y_{1}){\text{and}},(x_{2},y_{2})[/tex]

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m_{1}=\frac{7\frac{3}{4}-6\frac{1}{4}}{1\frac{1}{4}-\frac{3}{4}}=\frac{\frac{6}{4}}{\frac{2}{4}}=\frac{6}{2}=3\\\\ m_{1}=\frac{y-6\frac{1}{4}}{x-\frac{3}{4}}\\\\3=\frac{\frac{4y-25}{4}}{\frac{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}=\frac{y-7\frac{3}{4}}{x-1\frac{1}{4}}\\\\3=\frac{\frac{4y-31}{4}}{\frac{4x-5}{4}}[/tex]

→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.

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