Lines that go up and down

Do you agree that lines can go upward / direction or downward \ ? What's the direction of the following line?

Yes, upward. This line is represented by y = x .


Now, let's see a line going downward.

This is represented by y = -x

Do you see the difference between the equations representing lines going upward and downward? If yes, what is it?

Let me tell you.

The first equation representing the line going upward has a positive +x equation on the right-hand side.

The second equation representing the line going downward has a negative -x equation on the right-hand side.

Let's try to understand a little bit more about them

Whenever we write y = (something) times (x) , that something is the slope of the line. So we could rewrite y = x as

y = (1) times (x)

The slop of the equation here is 1 which indicates that when x increases by 1, our y value also increases by 1.

Similarly, for y = -x , we can rewrite as

y = (-1) times (x)

The slope of the equation is -1 which indicates that when x increases by 1, y decreases by 1.

These equations can be represented by some symbols through which we can talk and discuss more easily. So, we can say the above equations are represented by

y = (m) times (x)

Here, m is the slope of the equation which equals to +1 or -1 in our equations. So in short, we can say y = mx represents a line on the graph that might be going upward or downward depending on the value of m - the slope.

So next time you see an equation like this

y = -7x

You can say, oh the slope is -7 which means for every increase of x , y decreases by 7 times.

Or when you see an positive equation like this

y = 13x

You can say, the slope is +13 , and this means when x increases by 1, y also increases by 13 times that of x.

These lines we have discussed are very simple linear lines that go through the origin (0, 0) . Both the lines intercept y-axis at 0.

Why these equations are important to recognize and knowing how to plot them could reveal insightful data when applied to our real-life problems related to growth, budgeting and obviously other phenomena in the universe.

Next, we will talk about y intercepts.