Question

(2,1)(0,1)
Which of the following are in the proper point slope form?

y-1 = 0
y-1 = 0(x +2)
y = 0
y + 1 = 0(x-2)
undefined

Answer 1

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

For the points (2,1) and (0,1), the slope is 0 because the y-values are the same for both points (horizontal line).

Now let's check the given options:

1) y-1 = 0
This is not in the point-slope form. It is in the slope-intercept form where y is isolated on one side.

2) y-1 = 0(x + 2)
This is in the point-slope form. The slope is 0 and the point (2,1) is on the line.

3) y = 0
This is not in the point-slope form. There is no point-slope equation since the slope is 0 and there is no specific point given.

4) y + 1 = 0(x-2)
This is in the point-slope form. The slope is 0 and the point (2,1) is on the line.

5) undefined
This is not a valid option. You didn't provide any equation or expression for this option.

So the options that are in the proper point-slope form are:
- y-1 = 0(x + 2)
- y + 1 = 0(x-2)