question 7 of 25\nwhich point lies on the line with point - slope equation y - 2 = 5(x - 6)?\na. (-6…

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is (y - y_1=m(x - x_1)), where ((x_1,y_1)) is a point on the line and (m) is the slope of the line. In the given equation (y - 2=5(x - 6)), by comparing with the point - slope form (y - y_1=m(x - x_1)), we can see that (x_1 = 6) and (y_1=2).

Step2: Check the points

We need to check which of the given points has (x = 6) and (y = 2) (since ((x_1,y_1)=(6,2)) should lie on the line).

• For option A: ((-6,-2)), (x=-6\neq6) and (y = - 2\neq2), so it does not lie on the line.
• For option B: ((-6,2)), (x=-6\neq6), so it does not lie on the line.
• For option C: ((6,2)), (x = 6) and (y=2), which matches the ((x_1,y_1)) from the point - slope form, so this point lies on the line.
• For option D: ((6,-2)), (y=-2\neq2), so it does not lie on the line.

Answer:

C. (6, 2)