line ab passes through points a(-6, 6) and b(12, 3). if the equation of the line is written in slope…

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is (y = mx + b), where (m) is the slope and (b) is the y - intercept. We know that (m=-\frac{1}{6}), and we can use a point that the line passes through (either (A(-6,6)) or (B(12,3))) to find the value of (b). Let's use point (A(-6,6)). Substitute (x=-6), (y = 6) and (m=-\frac{1}{6}) into the equation (y=mx + b).

Step2: Substitute values into the equation

Substituting (x=-6), (y = 6) and (m =-\frac{1}{6}) into (y=mx + b), we get: (6=-\frac{1}{6}\times(-6)+b) First, calculate (-\frac{1}{6}\times(-6)). The product of two negative numbers is positive, and (\frac{1}{6}\times6 = 1). So the equation becomes: (6 = 1 + b)

Step3: Solve for (b)

To solve for (b), subtract 1 from both sides of the equation (6=1 + b). (b=6 - 1) (b = 5)

We can also verify with point (B(12,3)). Substitute (x = 12), (y=3) and (m=-\frac{1}{6}) into (y=mx + b). Substitute into (y=mx + b): (3=-\frac{1}{6}\times12 + b) Calculate (-\frac{1}{6}\times12=-2). Then the equation is (3=-2 + b). Add 2 to both sides: (b=3 + 2=5).

Answer:

5 (corresponding to the option "5")