For this case we have that by definition, the point-slope equation of a line 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 two points:
[tex](x_ {1}, y_ {1}): (- 5,7)\\(x_ {2}, y_ {2}): (- 4,0)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-7} {- 4 - (- 5)} = \frac {-7} {-4 + 5} = \frac {-7} {1} = - 7[/tex]
Thus, the equation is of the form:
[tex]y = -7x + b[/tex]
We substitute one of the points and find "b":
[tex]0 = -7 (-4) + b\\0 = 28 + b\\b = -28[/tex]
Finally, the equation is:
[tex]y = -7x-28[/tex]
Answer:
[tex]y = -7x-28[/tex]
