a line passes through the point (6, -1) and has a slope of -2. write an equation in slope - intercept form…

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is (y - y_1=m(x - x_1)), where (m) is the slope and ((x_1,y_1)) is a point on the line. Given (m=-2), (x_1 = 6), and (y_1=-1), we substitute these values into the formula: (y-(-1)=-2(x - 6)) (y + 1=-2(x - 6))

Step2: Expand the right - hand side

Using the distributive property (a(b - c)=ab-ac), where (a=-2), (b = x), and (c = 6) (y+1=-2x+12)

Step3: Solve for (y) (convert to slope - intercept form (y=mx + b))

Subtract 1 from both sides of the equation: (y=-2x+12 - 1) (y=-2x + 11)

Answer:

(y=-2x + 11)