Question

question 7 of 25
which point lies on the line with point - slope equation y - 2 = 5(x - 6)?
a. (-6, -2)
b. (-6, 2)
c. (6, 2)
d. (6, -2)

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

eq6\) and \(y = - 2
eq2\), so it does not lie on the line.

• For option B: \((-6,2)\), \(x=-6

eq6\), 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

eq2\), so it does not lie on the line.

Answer:

C. (6, 2)