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: Is the slope
b: Is the cut-off point with the y axis
According to the image we have that the line goes through the following points:
[tex](x_ {1}, y_ {1}) :( 0, -3)\\(x_ {2}, y_ {2}) :( 6,1)[/tex]
Then, the slope is of the form:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {1 - (- 3)} {6-0} = \frac {1 + 3} {6} = \frac {4} {6} = \frac {2} {3}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {2} {3} x + b[/tex]
We know that the cut-off point is[tex]b = -3,[/tex] finally the equation is:
[tex]y = \frac {2} {3} x-3[/tex]
Answer:
[tex]y = \frac {2} {3} x-3[/tex]
