Write in standard form an equation of the line with the given slope through the given point: slope = -4;(2,2)

To write an equation of a line in standard form, we need to use the slope-intercept form of a line (y = mx + b) where "m" represents the slope of the line.

The slope-intercept form of a line is given by:
y = mx + b

Given that the slope (m) is -4 and the point (2,2) is on the line, we can find the equation of the line as follows:

Step 1: Plug in the given slope (-4) and the coordinates of the point (2,2) into the slope-intercept form (y = mx + b):
2 = -4(2) + b

Step 2: Simplify the equation:
2 = -8 + b

Step 3: Solve for b by isolating it. Add 8 to both sides of the equation:
2 + 8 = b
10 = b

Step 4: Now we have the value of b, substitute it back into the slope-intercept form equation:
y = -4x + 10

Step 5: Rewrite the equation in standard form (Ax + By = C):
4x + y = 10

Therefore, the equation of the line with a slope of -4 through the point (2,2) is 4x + y = 10.