To find the equation of a line passing through a given point and having a given slope, we can use the point-slope form of the equation of a line. The point-slope form is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here:
- [tex]\((x_1, y_1)\)[/tex] is the given point the line passes through.
- [tex]\(m\)[/tex] is the slope of the line.
In this problem:
- The given point [tex]\((x_1, y_1)\)[/tex] is [tex]\((-1, 6)\)[/tex].
- The slope [tex]\(m\)[/tex] is [tex]\(-7\)[/tex].
Let's substitute these values into the point-slope form equation:
[tex]\[ y - 6 = -7(x - (-1)) \][/tex]
Simplifying the expression inside the parentheses:
[tex]\[ y - 6 = -7(x + 1) \][/tex]
Therefore, the equation of the line in point-slope form that passes through the point [tex]\((-1, 6)\)[/tex] and has a slope of [tex]\(-7\)[/tex] is:
[tex]\[ y - 6 = -7(x - 1) \][/tex]
