To find the equation of a line given a point it passes through and its slope, we use the point-slope form of a linear equation. The point-slope form is given by
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.
Given:
- The point [tex]\((-2, -2)\)[/tex]
- The slope [tex]\(m = -3\)[/tex]
Substitute the given point and slope into the point-slope form:
[tex]\[ y - (-2) = -3(x - (-2)) \][/tex]
Simplify the equation by handling the double negatives:
[tex]\[ y + 2 = -3(x + 2) \][/tex]
This equation,
[tex]\[ y + 2 = -3(x + 2) \][/tex]
is in the point-slope form and represents the line that passes through the point [tex]\((-2, -2)\)[/tex] with a slope of [tex]\(-3\)[/tex].
