Question

Table

Answer 1

Answer:

The graph of the the equation $\:y=x+1$ 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:

• (2, 3)

• (4, 5)

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(2,\:3\right),\:\left(x_2,\:y_2\right)=\left(4,\:5\right)$

$m=\frac{5-3}{4-2}$

$m=1$

As the slope-intercept form is given by

$y\:=\:mx+b$

Plugging any point, let say (2, 3) and m = 1 in the slope-intercept form to get the value of 'b' (y-intercept).

$y\:=\:mx+b$

$3\:=\:\left(1\right)2+b$

$\mathrm{Switch\:sides}$

$\left(1\right)\cdot \:2+b=3$

$2+b=3$

$\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}$

$2+b-2=3-2$

$b=1$

So the equation for the data presented in table will be:

$y\:=\:mx+b$

• m = 1

• b = 1

Plugging the values in the equation

$y\:=\:mx+b$

$y\:=\:\left(1\right)x+1$

$\:y=x+1$

Where

the slope = m = 1

y-intercept = b = 1

The graph of the the equation $\:y=x+1$ is also attached below.