For this case we have that by definition, the equation of the line in 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-off point with the y axis
We have the following points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 6,13)\\(x_ {2}, y_ {2}): (7900,5)[/tex]
We find the slope of the line:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5-13} {7900-6} = \frac {-8} {7894} = - \frac {4} {3947}[/tex]
Thus, the equation of the line is of the form:
[tex]y = - \frac {4} {3947} x + b[/tex]
We substitute one of the points and find b:
[tex]13 = - \frac {4} {3947} (6) + b\\13 = - \frac {24} {3947} + b\\13+ \frac {24} {3947} = b\\b = \frac {51335} {3947}[/tex]
Finally, the equation is:
[tex]y = - \frac {4} {3947} x + \frac {51335} {3947}[/tex]
Answer:
[tex]y = - \frac {4} {3947} x + \frac {51335} {3947}[/tex]
