For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut point with the y axis
According to the graph, we have the points:
[tex](x_ {1}, y_ {1}) :( 2,0)\\(x_ {2}, y_ {2}) :( 0,4)[/tex]
We find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {4-0} {0-2} = \frac {4} {- 2} = -2[/tex]
Thus, the equation is of the form:
[tex]y = -2x + b[/tex]
We substitute a point and find b:
[tex]0 = -2 (2) + b\\0 = -4 + b\\b = 4[/tex]
Finally we have:
[tex]y = -2x + 4[/tex]
Answer:
[tex]y = -2x + 4[/tex]
