2.6.1 Exploring the Slope of a Line
If a line has the form f(x)=mx, then if
- m>0, the line slopes upwards or increases
- m<0, the line slopes downwards or decreases
- 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
the graph 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.
