Answer:
To find the equation of a line with a given slope and passing through a specific point, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
Where (x1, y1) represents the coordinates of the given point, and m represents the slope of the line.
In this case, the slope (m) is given as -5, and the point (2, -6) is on the line. Substituting these values into the point-slope form, we have:
y - (-6) = -5(x - 2)
Simplifying further:
y + 6 = -5x + 10
Rearranging the equation to match the desired form (y = mx + b), we subtract 6 from both sides:
y = -5x + 4
Therefore, the equation of the line with a slope of -5 and passing through the point (2, -6) is y = -5x + 4.
Explanation: