For this case we have that by definition, the equation of a 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
The slope can be found using the formula:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}): (-2,7)\\(x_ {2}, y_ {2}): (4,1)[/tex]
Thus, the slope is:
[tex]m = \frac {1-7} {4 - (- 2)} = \frac {-6} {4 + 2} = \frac {-6} {6} = - 1[/tex]
Thus, the equation is of the form:
[tex]y = -x + b[/tex]
We substitute a point and find "b":
[tex]1 = -4 + b\\1 + 4 = b\\b = 5[/tex]
Finally, the equation is:
[tex]y = -x + 5[/tex]
Answer:
[tex]y = -x + 5[/tex]
