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's the slope
b: It is the cut-off point with the y axis
We have two points through which the line passes, so we can find the slope:
[tex](x_ {1}, y_ {1}) :( 4, -4)\\(x_ {2}, y_ {2}) :( 8, -10)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-10 - (- 4)} {8-4} = \frac {-10+ 4} {4} = \frac {-6} {4} = - \frac {3} {2}[/tex]
Thus, the equation is of the form:
[tex]y = - \frac {3} {2} x + b[/tex]
We substitute one of the points and find "b":
[tex]-4 = - \frac {3} {2} (4) + b\\-4 = - \frac {12} {2} + b\\-4 + 6 = b\\b = 2[/tex]
Finally, the equation is of the form:
[tex]y = - \frac {3} {2} +2[/tex]
ANswer:
[tex]y = - \frac {3} {2} +2[/tex]
