[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Here's the solution ~
Let's consider two points (-2 , 0) and (0 , 2) on the line to find the slope (m) :
[tex]\qquad \sf \dashrightarrow \: m = \dfrac{y_2 - y_1}{x_2 - x _1} [/tex]
[tex]\qquad \sf \dashrightarrow \: m = \dfrac{2 - 0}{0 - ( - 2)} [/tex]
[tex]\qquad \sf \dashrightarrow \: m = \dfrac{2}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: m = 1[/tex]
And, now let's observe the graph ; the distance of origin (sign included) from the point where the line cuts y - axis will be the y - intercept (c) .
That is : 2 - 0 = 2 units
Next step :
As we know any line can be expressed through slope intercept form ;
[tex]\qquad \sf \dashrightarrow \: y = mx + c[/tex]
Here, m = slope and c = y - intercept [ already got the values ]
Now, use the values to find the equation ;
[tex]\qquad \sf \dashrightarrow \: y = (1 \times x) + 2[/tex]
[tex]\qquad \sf \dashrightarrow \: y = x + 2[/tex]
Therefore the required equation is ~
[tex] \large \qquad \qquad \sf \boxed{\boxed{ \sf y = x + 2}}[/tex]
