# 2.6.1 Exploring the Slope of a Line

If a line has the form f(x)=mx, then if

1. m>0, the line slopes upwards or increases
2. m<0, the line slopes downwards or decreases
3. m=0, the line is horizontal or constant

We have now studied one particular algebraic equation that graphically looked like a straight line. Can we use what we learned from that particular example to find a general equation of a line? Based on what we saw previously, it seems that when our equation has a constant term times x, our graph will look like a straight line; the .69x meant that as x increased by 1 unit, the y values increased by a constant .69. With this in mind, we can begin to study mathematical creatures of the form "mx" where m is a constant and try to find some patterns.

What does the m do? Let's plug in a couple of different values for m and try to see what's going on in the graph. And, to be efficient, we should note that to draw a straight line, we only need to sketch two points, so we'll just find two points on the graph and then connect the dots.

f(x)= 2x

x y
1
2

Plot the points on graph paper, connecting the dots, and then compare your answer to
the graph below.

Let's try one more example together:

f(x) = -3x

x y
1
2

Plot the points on graph paper, connecting the dots, and then compare your answer to

Now use the to play around with different values of m. By exploring specific values, come to a conclusion about how m affects the graph and be ready to answer some questions below.

Based on what you saw while using the graphing tool:

When m>0, y values get when we move left to right on the graph.

When m<0, the y values get as we move from left to right on the graph.

The line is horizontal when m = .

We'll now study our constant, m, also known as the slope of a line, a bit more in the next section.