Answer:
[tex]2x-y+1=0[/tex]
Step-by-step explanation:
The given points are,
[tex](-2,-3),(-1,-1),(0,1),(1,3),(2,5)[/tex]
The difference in x coordinates is 1 and the difference in y coordinates is also 1. As change in both x and y are same and constant, so graph will be a straight line.
Plotting the points on the Cartesian coordinates, we get a straight line.
Applying two point formula, taking (-2,-3), (-1,-1), we get
[tex]\Rightarrow \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}[/tex]
[tex]\Rightarrow \dfrac{y+3}{-1+3}=\dfrac{x+2}{-1+2}[/tex]
[tex]\Rightarrow \dfrac{y+3}{2}=\dfrac{x+2}{1}[/tex]
[tex]\Rightarrow y+3=2(x+2)[/tex]
[tex]\Rightarrow y+3=2x+4[/tex]
[tex]\Rightarrow 2x-y+1=0[/tex]
