Question

Graph the function represented in the table on the coordinate plane.

Answer 1

First find out the function for the given table.
Find the slope.
m= (y2-y1)/(x2-x1)
m=(-1-(-3)) / (-1-(-2))
m=(-1+3) / (-1+2)
m=2/1
m=2
Now equation of line:
y-y1=m(x-x1)
y-(-3)=2(x-(-2))
y+3=2(x+2)
y+3=2x+4
y=2x+1
Now plot these points on the graph, we get the attached graph.

Answer 2

The ordered pair in the coordinate plane is

x :  -2    -1     0       1       2

y :   -3     -1     1       3       5

First we will check whether these points are collinear or not by plotting it into two dimensional plane.

As without drawing the graph you can also check whether these points are collinear or not , as x values increases by same number i.e (+1) and y value increases by same number i.e (+2).

So, these points are collinear.

Equation of line passing through all the five points can be get by the method of equation of line passing through two points.

$\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\frac{y+3}{x+2}=\frac{-1+3}{-1+2}\\\\ y+3 =2 (x+2)\\\\y +3 = 2 x + 4\\\\ 2 x -y +1=0$