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 is the slope of the line
b: It is the cut-off point with the y axis
To find the slope, we need two points, according to the graph we have:
[tex](x_ {1}, y_ {1}) :( 0,3)\\(x_ {2}, y_ {2}) :( 1,0)[/tex]
The slope is:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-3} {1-0} = \frac {-3} {1} = -3[/tex]
Therefore, the equation is of the form:
[tex]y = -3x + b[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:
[tex]y = -3x + b[/tex]
We substitute the point through which the line passes and find "b":
[tex]3 = -3 (-2) + b\\3 = 6 + b\\3-6 = b\\b = -3[/tex]
Finally, the equation is:
[tex]y = -3x-3[/tex]
ANswer:
[tex]y = -3x-3[/tex]
