Respuesta :
You can see that there is a proportional relationship between X and Y because every 6 of X decreases 3 in Y. In that way you can say is a linear relationship and you can construct a linear equation: Now, to calculate the equation you use: (Y - y1) = y2 - y1 (X - x1) x2 - x1 Let's peek two pairs (1,-4) and (7,-7) (Y - (-4)) = (-7 - (-4)) (X - 1) (7 - 1) Y + 4 = -3 (X - 1) 6 If you want to express the equation as aX + bY + C = 0 Y + 1/2 X + 7/2 = 0 If you want to express the equation as Y= ax + b Y = -1/2X - 7/2
Answer:
Yes, the relationship shown by the data linear.
The equation is given by:
[tex]y=\dfrac{-1}{2}x-\dfrac{7}{2}[/tex]
Step-by-step explanation:
The table of values is given by:
x y
1 -4
7 -7
13 -10
19 -13
We know that the difference in each of the x-value is: 6
( Since, 7-1=6
13-7=6
19-13=6)
and if the difference in the each of the y-value is same then the relationship is linear.
( Since, a table of values represent a linear relationship if the rate of change is constant.
i.e. the ratio of change in y-values to the change in x-values)
Hence, we find the difference in y-value:
-7-(-4)= -3
-10-(-7)= -3
-13-(-10)= -3
Since, the difference in y-value is constant.
Hence, the relationship is linear.
Also, we know that the equation of the line will pass through (1,-4) and (7,-7)
Hence, the equation of line is calculated by:
[tex]y-(-4)=\dfrac{-7-(-4)}{7-1}\times (x-1)\\\\i.e.\\\\y+4=\dfrac{-3}{6}\times (x-1)\\\\i.e.\\\\y+4=\dfrac{-1}{2}\times (x-1)\\\\i.e.\\\\y+4=\dfrac{-1}{2}x+\dfrac{1}{2}\\\\i.e.\\\\y=\dfrac{-1}{2}x+\dfrac{1}{2}-4\\\\i.e.\\\\y=\dfrac{-1}{2}x-\dfrac{7}{2}[/tex]
