Explain the difference between a line with zero slope and a line with an undefined slope

In algebra, we use the word slope to describe how steep a line is. Slope can be found using the ratio rise over run between any two points on that line.

A very common mistake made when dealing with slope is to think that a line with a slope of 0 is the same as a line with an undefined slope. However, they're not the same and are very different.

Take a look at the first image I provided.

To get from A to point B along this line, we rise 0 units and run 2 units. So our slope or rise over run is 0/3 which simplifies to 0. In fact, for any horizontal or flat line, the slope is always 0.

Take a look at the second image I provided.

To get from point A to point B along this line, we go down 5 units so our rise is -5. Our run however is 0 so our slope or rise over run is -5/0. It's important to understand that any number divided by zero is undefined so we say that this line is undefined or it has no slope.

In fact, any line that is vertical or straight up and down has no slope.

To summarize, it's important to understand that difference between and a slope of zero and no slope. Zero means that the line is flat or horizontal. No slope means we can't describe its slope using a number because the line is vertical and its slope is undefined.

your answer would be 10x - 1

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3