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 = -2[/tex]
Then, the equation is of the form:
[tex]y = -2x + b[/tex]
We substitute the point[tex](x, y): (- 5, -3)[/tex]and find "b":
[tex]-3 = -2 (-5) + b\\-3 = 10 + b\\-3-10 = b\\b = -13[/tex]
Finally, the equation is:
[tex]y = -2x-13[/tex]
To graph we place the points [tex](-5, -3)[/tex]and[tex](0, -13)[/tex] on the coordinate axis and join the points by a line.
ANswer:
[tex]y = -2x-13[/tex]
The graphic is attached.
