Let's review what we know about the algebra of straight lines so far:

1. Every straight line with a slope has constant slope.

2. We can find the slope of a line from any two points on it by dividing the difference in the y-values by the difference in the x-values. That is, as we go from one point on the line to another, the slope is

3. There is one kind of line for which this slope finding process does not work: The change in x between any two points of a vertical line is 0, and we can't divide by 0.

4. If the straight line goes through the origin, we can use (0, 0) as one of the points for finding slope. Then, when we go to another point on this line, the change in y is just the y-value of that point and the change in x is just its x-value. This makes it easy to find the slope of a line through the origin.

5. The slope of a line is a rate of change. It tells us how many units to go up or down for each unit we go to the right (that is, in the positive x direction) in moving from one point to another on the line.

6. In particular, if we start at (0, 0) on a line through the origin and want to go to any other point on it, then the y-value of that other point can be found by multiplying its x-value by the slope.

7. In the language of algebra, this means that the coordinates of every point on a straight line through the origin (except for the y-axis) must satisfy the equation

y = mx

where m is the slope of the line.

Statement 5 above describes how slope works in the positive x-direction from the origin. Explain how this statement leads to Statement 6, which applies to points in either x-direction from the origin.

Learning Outcomes
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After studying this section, you will be able to:

Use a graphing calculator to explore the graphs of lines and to create straight line patterns;

Describe how changing a number in a linear equation alters the position of its graph.