For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the figure, the line goes through the following points:
[tex](x_ {1}, y_ {1}) :( 2,3)\\(x_ {2}, y_ {2}) :( 0,2)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {2-3} {0-2} = \frac {-1} {- 2} = \frac {1} {2}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {1} {2} x + b[/tex]
We substitute a point and find "b":
[tex]2 = \frac {1} {2} (0) + b\\2 = b[/tex]
Finally, the equation is:
[tex]y = \frac {1} {2} x + 2[/tex]
ANswer:
[tex]y = \frac {1} {2} x + 2[/tex]
