Respuesta :
We are given table of input and output:
input output
3 5
4 7
6 11
11 21
We take x coordinate as input values and y-coordinates as output.
So, we can take two two coordinates from the given table (3,5) and (4,7).
Now, we need to find the slope between those two coordinates:
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(3,\:5\right),\:\left(x_2,\:y_2\right)=\left(4,\:7\right)[/tex]
[tex]m=\frac{7-5}{4-3}[/tex]
[tex]m=2[/tex]
Now, applying point slope formula
y-y1 = m(x-x1)
y - 5 = 2(x-3)
y -5 = 2x -6
Adding 5 on both sides, we get
y -5+5 = 2x -6+5
y = 2x -1.
Therefore, required eqution is y=2x-1.
In order to prove the equation for the table, we can plug x=3,4,6 and 11 in the euqation.
y=2(3)-1 = 6 -1 = 5
y =2(4) -1 = 8 - 1 = 7
y =2(6) - 1 = 12 -1 = 11.
y = 2(11) - 1 = 22-1 = 21.
Each input in table gives same vaule of output given in the table.
