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 data of the statement we have to:
[tex]m = \frac {1} {4}[/tex]
Then, the equation is of the form:
[tex]y = \frac {1} {4} x + b[/tex]
We substitute the point [tex](x, y): (- 2, -6)[/tex] and find "b":
[tex]-6 = \frac {1} {4} (- 2) + b\\-6 = - \frac {1} {2} + b\\-6+ \frac {1} {2} = b\\b = \frac {-12 + 1} {2}\\b = - \frac {11} {2}[/tex]
Finally, the equation is:
[tex]y = \frac {1} {4} x- \frac {11} {2}[/tex]
ANswer:
[tex]y = \frac {1} {4} x- \frac {11} {2}[/tex]
