Question

Which equation is in slope intercept form and represents a line with slope 0 through the point (2,3)

Answer 1

The slope is m = 0 and the line goes through the point (x,y) = (2,3). So x = 2 pairs up with y = 3.

Plug m = 0, x = 2, y = 3 into the equation below. Then solve for b
y = mx+b
3 = 0*2+b
3 = 0+b
3 = b
b = 3

So if m = 0 and b = 3, then
y = mx+b
y = 0*x+3
y = 0+3
y = 3
is the equation of this line. This line is completely horizontal going through points like (0,3), (1,3), (2,3), etc. Every point on this line has a y coordinate of 3. The x coordinate can be any number you want.

Answer: Choice C) y = 3

Answer 2

Any line with slope 0 is horiz.  This particular line is to pass thru (2,3), so the y-intercept, b, is 3.  The equation of the line is then y=3.  x is "silent;" it does not appear in this equation.

You could also write y = 3 as    y = 0(x) + 3.