For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
Where:
m: Is the slope
b: Is the cut-off point with the y axis
According to the data of the statement we have two points through which the line passes:
[tex](x_ {1}, y_ {1}): (0, -2)\\(x_ {2}, y_ {2}): (6,0)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0 - (- 2)} {6-0} = \frac {0 + 2} {6} = \frac {2} {6} = \frac {1} {3}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {1} {3} x + b[/tex]
We substitute one of the points and find "b":
[tex]-2 = \frac {1} {3} (0) + b\\-2 = b[/tex]
Finally, the equation is:
[tex]y = \frac {1} {3}x -2[/tex]
Answer:
[tex]y = \frac {1} {3}x -2[/tex]
