# How do I write equations that has a slope of 1/2, 0, and undefined? I do not understand. Please write out the solutions. Thanks for your help

enotechris | College Teacher | (Level 2) Senior Educator

Posted on

The point slope formula is:

1)  (y - y1) = m(x - x1)

where m represents the value of the slope, and (x,y) and (x1,y1) represent two points on a graph. Rearranging the equation gives:

2)   m = (y - y1) / (x - x1)

If you have a slope of zero,

3)    0 = (y - y1) / (x - x1)

it means the numerator (y - y1) must also reduce to 0, which means the value of y and y1 must be the same.  Zero divided by anything is always zero:

4)    0 = 0 / (x - x1)

A zero slope means the line has a value of y, is parallel to the x axis, and never intersects with it.

If the slope is undefined, it implies division by zero, which means x and x1 are the same value:

1)   m = (y - y1) / (x - x1)

2)   m = (y - y1) / 0

What that means is that the line has no slope; it's a vertical line running parallel to the y axis at value x.

For slope 1/2:

1)   1/2 = (y - y1) / (x - x1)

Which means that if the value of y changes by 1 unit, the value of x changes by 2 units, or if the rise (y value) changes by 1, the run (x value) changes by 2.

Sources: