For this case we have that by definition, the equation of a 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 image, the line goes through the following points:
[tex](x_ {1}, y_ {1}): (2,1)\\(x_ {2}, y_ {2}): (0,4)[/tex]
So, the slope is:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {4-1} {0-2} = \frac {3} {- 2} = - \frac {3} {2}[/tex]
Thus, the equation is of the form:
[tex]y = - \frac {3} {2} x + b[/tex]
We substitute a point and find "b":
[tex]4 = -\frac {3} {2} (0) + b\\4 = b[/tex]
Finally, the equation is:
[tex]y = - \frac {3} {2} x + 4[/tex]
Answer:
[tex]y = - \frac {3} {2} x + 4[/tex]
