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 is the slope of the line
b: It is the cut-off point with the y axis
We have the following points:
[tex](x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): (- 2, -9)[/tex]
We can find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-9-6} {- 2-4} = \frac {-15} {- 6} = \frac {5} {2}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {5} {2} x + b[/tex]
We substitute one of the points and find "b":
[tex]6 = \frac {5} {2} (4) + b\\6 = 10 + b\\6-10 = b\\b = -4[/tex]
Finally, the equation is:
[tex]y = \frac {5} {2} x-4[/tex]
Thus, it is observed that the lines have the same y-intercept
Answer:
Option D
