To find the equation of a line with a given slope and passing through a given point, you can use the point-slope form of a linear equation.
The point-slope form is given by: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
In this case, the slope (m) is -3, and the given point is (1, -2).
Substituting these values into the point-slope form, we get: y - (-2) = -3(x - 1).
Simplifying, we have: y + 2 = -3x + 3.
To rewrite the equation in slope-intercept form (y = mx + b), we need to isolate y on one side of the equation.
Subtracting 2 from both sides of the equation, we get: y = -3x + 1.
Therefore, the equation of the line with slope -3 that goes through the point (1, -2) is y = -3x + 1.
Note: The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept (the value of y when x = 0). In this case, the y-intercept is 1.