Answer:
The graph of the the equation [tex]\:y=x+1[/tex] is also attached below.
Step-by-step explanation:
Here is the given table
x y
2 3
4 5
6 7
8 9
10 11
Taking any two points:
[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(2,\:3\right),\:\left(x_2,\:y_2\right)=\left(4,\:5\right)[/tex]
[tex]m=\frac{5-3}{4-2}[/tex]
[tex]m=1[/tex]
As the slope-intercept form is given by
[tex]y\:=\:mx+b[/tex]
Plugging any point, let say (2, 3) and m = 1 in the slope-intercept form to get the value of 'b' (y-intercept).
[tex]y\:=\:mx+b[/tex]
[tex]3\:=\:\left(1\right)2+b[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]\left(1\right)\cdot \:2+b=3[/tex]
[tex]2+b=3[/tex]
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}[/tex]
[tex]2+b-2=3-2[/tex]
[tex]b=1[/tex]
So the equation for the data presented in table will be:
[tex]y\:=\:mx+b[/tex]
Plugging the values in the equation
[tex]y\:=\:mx+b[/tex]
[tex]y\:=\:\left(1\right)x+1[/tex]
[tex]\:y=x+1[/tex]
Where
the slope = m = 1
y-intercept = b = 1
The graph of the the equation [tex]\:y=x+1[/tex] is also attached below.
