For this case we have that by definition, the equation of the 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 the following points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 0, -7)\\(x_ {2}, y_ {2}) :( 5,12)[/tex]
Thus, the slope of the line is:
[tex]m = \frac {y- {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {12 - (- 7)} {5-0} = \frac {12 + 7 } {5} = \frac {19} {5}[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:
[tex]y = \frac {19} {5}x + b[/tex]
Answer:
[tex]y = \frac {19} {5}x + b[/tex]
